Solve 3

Solve quadratic equation:

(6n+1) (4n-1) = 3n²

Correct answer:

n₁ =  0.271
n₂ =  -0.1757

Step-by-step explanation:

$$\begin{gathered} (6n+1)(4n-1)=3n^2 \\ 21n^2-2n-1=0 \\ a=21;b=-2;c=-1 \\ D=b^2-4ac=2^2-4\cdot 21\cdot (-1)=88 \\ D>0 \\ {n}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{2\pm \sqrt{88}}{42}}={\displaystyle \frac{2\pm 2\sqrt{22}}{42}} \\ {n}_{1,2}=0.04761905\pm 0.22335313142 \\ {n}_1=0.270972179039 \\ {n}_2=-0.175734083801 \\ \text{ Factored form of the equation: } \\ 21(n-0.270972179039)(n+0.175734083801)=0 \\ {n}_1=0.271 \end{gathered}$$

Our quadratic equation calculator calculates it.

$n_2=(-0.1757)=-0.1757$

Try another example

Related math problems and questions:

• Sequence
  Write the first 6 members of this sequence: a₁ = 5 a₂ = 7 a_n+2 = a_n+1 +2 a_n
• Fruits
  Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all?
• Equation
  Solve equation and check the result: 1.4x - 3/2 + x - 9,8 = x + 0,4/3 - 7 + 1,6/6
• Quadratic function 2
  Which of the points belong function f:y= 2x²- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
• VCP equation
  Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
• Boats
  Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
• Median or middle
  The number of hours of television watched per day by a sample of 28 people is given below: 4, 1, 5, 5, 2, 5, 4, 4, 2, 3, 6, 8, 3, 5, 2, 0, 3, 5, 9, 4, 5, 2, 1, 3, 4, 7, 2, 9 What is the median value?
• Evaluate
  The division of numbers 6 and 3 increase by-product of the numbers 115 and 0.1
• Simple equation
  Solve the following simple equation: 2. (4x + 3) = 2-5. (1-x)
• Solve equation
  solve equation: [(a²)+3]^1/2 + [(a²)-3]^1/2 = 5
• Cancel fractions
  Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
• Watching TV
  One evening 2/3 students watch TV. Of those students, 3/8 watched a reality show. Of the students that watched the show, 1/4 of them recorded it. What fraction of the students watched and recorded reality tv.
• Quadratic equation
  Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
• Quadratic function
  Write the equation of the quadratic function, which includes points A (-1, 10), B (2, 19), C (1,4)
• Intersect and conjuction
  Let U={1,2,3,4,5,6} A={1,3,5} B={2,4,6} C={3,6} Find the following. 1. )AUB 2. )A'UB'
• Four pavers
  Four pavers would pave the square in 18 days. How many pavers do you need to add to done work in 12 days?
• Three digits number 2
  Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one positions is one of the numbers 1,3,4, on the place of hundreds 4 or 2.