3x^2+4x-24=0

Simple and best practice solution for 3x^2+4x-24=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3x^2+4x-24=0 equation: 


Simplifying
3x2 + 4x + -24 = 0

Reorder the terms:
-24 + 4x + 3x2 = 0

Solving
-24 + 4x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-8 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 1.333333333x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 1.333333333x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 1.333333333x + x2 = 0 + 8
1.333333333x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
1.333333333x + x2 = 8

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 8 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 8 + 0.4444444442

Combine like terms: 8 + 0.4444444442 = 8.4444444442
0.4444444442 + 1.333333333x + x2 = 8.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 8.4444444442

Calculate the square root of the right side: 2.905932629

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.905932629 and -2.905932629.


Subproblem 1
x + 0.6666666665 = 2.905932629

Simplifying
x + 0.6666666665 = 2.905932629

Reorder the terms:
0.6666666665 + x = 2.905932629

Solving
0.6666666665 + x = 2.905932629

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 2.905932629 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 2.905932629 + -0.6666666665
x = 2.905932629 + -0.6666666665

Combine like terms: 2.905932629 + -0.6666666665 = 2.2392659625
x = 2.2392659625

Simplifying
x = 2.2392659625


Subproblem 2
x + 0.6666666665 = -2.905932629

Simplifying
x + 0.6666666665 = -2.905932629

Reorder the terms:
0.6666666665 + x = -2.905932629

Solving
0.6666666665 + x = -2.905932629

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -2.905932629 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -2.905932629 + -0.6666666665
x = -2.905932629 + -0.6666666665

Combine like terms: -2.905932629 + -0.6666666665 = -3.5725992955
x = -3.5725992955

Simplifying
x = -3.5725992955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2392659625, -3.5725992955}

See similar equations:

| x^2-2x-28=0 | | 0.1(0.1x+0.9)=-0.5 | | x(x-2)=28 | | 2c+7=4c-7 | | -6(-9x-15)=504 | | -560=-10(-7x-14) | | 2x^2-14x-74=0 | | 4ln(2x+8)=12 | | 3(2e-.3)=19.4-e | | -5(-8x+14)=370 | | 3ln(4x+4)=10 | | (5r+7s)(5r-7s)= | | x(x+5)=150 | | -438=-6(-5x+18) | | 5(-6x+7)=305 | | 65=5(6x-17) | | 20.6+2.1w=-8.2w | | 5x+3(5x+16)=-72 | | -187=5x-4(7x+18) | | 129=5x+3(-7x-9) | | y=-5x+39 | | -3x-3(-3x+15)=-15 | | -128=3x-2(6x+10) | | -105=-5x-3(3x+7) | | -4x-5(2x-17)=-27 | | 5x+y=23 | | Y=-2X^3+3X+6 | | 25x+8y=65 | | 79=2x+7(-x+7) | | 122=7x-3(-5x-4) | | 2x+6(-5x-10)=108 | | a-3.4=5 |

Equations solver categories