3x^2+9x-6=0

Simple and best practice solution for 3x^2+9x-6=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+9x-6=0 equation: 


Simplifying
3x2 + 9x + -6 = 0

Reorder the terms:
-6 + 9x + 3x2 = 0

Solving
-6 + 9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 3x + x2 = 0

Solving
-2 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x + x2 = 0 + 2
3x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3x + x2 = 2

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3x + x2 = 4.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + 1.5 = 2.061552813

Simplifying
x + 1.5 = 2.061552813

Reorder the terms:
1.5 + x = 2.061552813

Solving
1.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.061552813 + -1.5
x = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
x = 0.561552813

Simplifying
x = 0.561552813


Subproblem 2
x + 1.5 = -2.061552813

Simplifying
x + 1.5 = -2.061552813

Reorder the terms:
1.5 + x = -2.061552813

Solving
1.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.061552813 + -1.5
x = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
x = -3.561552813

Simplifying
x = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.561552813, -3.561552813}
Solution
x = {0.561552813, -3.561552813}

See similar equations:

| 8t-5+2t=5+5t-12 | | -20=-2x+6x | | 2n-3x+5x-n= | | 4+ln(x-1)=5 | | 9(x+4)=9x | | 45+3d=5 | | 4(x-7)-2x+20=12 | | 3x=1x+15 | | 60-2j=40 | | -3=9-x | | 4x^2=-7x-2 | | 6(y+42)-15=-13 | | 14.5x+4x+4x=259 | | 10+2x=x | | 3(5x-7)=66 | | 5x+19x-3=6(4x+2) | | 7x=3x+48 | | b-24=16-3b | | 32x-16=8(4x-2) | | 1x+5=0 | | -4(4x+3)=16x+12 | | 29+29= | | 34x+80=34x+53 | | 3.0+0.2g=3.8 | | 2x(x+1)+3=7 | | 58/2= | | -2-12=m | | 5-4m+8+2m=17 | | -2(x+2)=-38 | | -x+7=2 | | 3x+x+1=9x-5x+1 | | 5n-7ifn=4 |

Equations solver categories