Solve 3

Solve quadratic equation:

(6n+1) (4n-1) = 3n2

Result

n1 =  0.271
n2 =  -0.176

Solution:

 21n2−2n−1=0  a=21;b=−2;c=−1 D=b2−4ac=22−4⋅21⋅(−1)=88 D>0  n1,2=−b±D2a=2±8842=2±22242 n1,2=0.04761905±0.22335313142016 n1=0.27097217903921 n2=−0.17573408380112   Factored form of the equation:  21(n−0.27097217903921)(n+0.17573408380112)=0  n1=0.271≐0.271=0.271 \ \\ 21n^2 -2n -1=0 \ \\ \ \\ a=21; b=-2; c=-1 \ \\ D=b^2 - 4ac=2^2 - 4\cdot 21 \cdot (-1)=88 \ \\ D>0 \ \\ \ \\ n_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 2 \pm \sqrt{ 88 } }{ 42 }=\dfrac{ 2 \pm 2 \sqrt{ 22 } }{ 42 } \ \\ n_{1,2}=0.04761905 \pm 0.22335313142016 \ \\ n_{1}=0.27097217903921 \ \\ n_{2}=-0.17573408380112 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 21 (n -0.27097217903921) (n +0.17573408380112)=0 \ \\ \ \\ n_{1}=0.271 \doteq 0.271=0.271

Checkout calculation with our calculator of quadratic equations.

n2=(−0.1757)≐−0.1757=−0.176n_{2}=(-0.1757) \doteq -0.1757=-0.176

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  2. Variation equation
    fun2_4 Solve combinatorics equation: V(2, x+8)=72
  3. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  4. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  5. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  6. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  7. Cinema 4
    cinema_2 In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?
  8. Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160
  9. Quadratic inequation
    eq2_8 If 5x + x² > 100, then x is not
  10. Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  11. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  12. Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  13. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  14. Tubes
    pipes_1 Iron tubes in the warehouse are stored in layers so that each tube top layer fit into the gaps of the lower layer. How many layers are needed to deposit 100 tubes if top layer has 9 tubes? How many tubes are in bottom layer of tubes?
  15. Quadratic equation
    Parabola_tangent Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
  16. The product
    eq222 The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?