Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.

Result

x1 =  2
x2 =  -0.667

#### Solution:

$\ \\ 3x^2-4x+(-4)=0 \ \\ 3x^2 -4x -4=0 \ \\ \ \\ a=3; b=-4; c=-4 \ \\ D=b^2 - 4ac=4^2 - 4\cdot 3 \cdot (-4)=64 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 4 \pm \sqrt{ 64 } }{ 6 } \ \\ x_{1,2}=\dfrac{ 4 \pm 8 }{ 6 } \ \\ x_{1,2}=0.66666667 \pm 1.3333333333333 \ \\ x_{1}=2 \ \\ x_{2}=-0.66666666666667 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 3 (x -2) (x +0.66666666666667)=0 \ \\ x_{1}=2$

Checkout calculation with our calculator of quadratic equations.

$x_{2}=(-0.6667)=- \dfrac{ 2 }{ 3 } \doteq -0.6667 \doteq -0.667$

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...):

Be the first to comment!

Tips to related online calculators

## Next similar math problems:

1. Equation 23
Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
2. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
4. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
5. Discriminant
Determine the discriminant of the equation: ?
6. Variations 4/2
Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition.
7. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
8. Combinations
From how many elements we can create 990 combinations 2nd class without repeating?
9. Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
Which of the points belong function f:y= 2x2- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
11. Tubes
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?
12. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
13. Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
14. 75th percentile (quartille Q3)
Find 75th percentile for 30,42,42,46,46,46,50,50,54
15. Sequence
Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
16. Sequence 3
Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
17. Theorem prove
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?