6x^2-20x-30=0

Simple and best practice solution for 6x^2-20x-30=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 6x^2-20x-30=0 equation: 


Simplifying
6x2 + -20x + -30 = 0

Reorder the terms:
-30 + -20x + 6x2 = 0

Solving
-30 + -20x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -10x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
-15 + -10x + 3x2 = 0

Solving
-15 + -10x + 3x2 = 0

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

Divide each side by '3'.
-5 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -3.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3.333333333x + x2 = 0 + 5
-3.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3.333333333x + x2 = 5

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 5 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 5 + 2.777777779

Combine like terms: 5 + 2.777777779 = 7.777777779
2.777777779 + -3.333333333x + x2 = 7.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 7.777777779

Calculate the square root of the right side: 2.788866755

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.788866755 and -2.788866755.


Subproblem 1
x + -1.666666667 = 2.788866755

Simplifying
x + -1.666666667 = 2.788866755

Reorder the terms:
-1.666666667 + x = 2.788866755

Solving
-1.666666667 + x = 2.788866755

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.788866755 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.788866755 + 1.666666667
x = 2.788866755 + 1.666666667

Combine like terms: 2.788866755 + 1.666666667 = 4.455533422
x = 4.455533422

Simplifying
x = 4.455533422


Subproblem 2
x + -1.666666667 = -2.788866755

Simplifying
x + -1.666666667 = -2.788866755

Reorder the terms:
-1.666666667 + x = -2.788866755

Solving
-1.666666667 + x = -2.788866755

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.788866755 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.788866755 + 1.666666667
x = -2.788866755 + 1.666666667

Combine like terms: -2.788866755 + 1.666666667 = -1.122200088
x = -1.122200088

Simplifying
x = -1.122200088


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.455533422, -1.122200088}
Solution
x = {4.455533422, -1.122200088}

See similar equations:

| 7x^2-1+50x-8=0 | | T=c(8+AB) | | 6y+4x=110 | | X^3=-50 | | -9+18=m-4 | | 1.5d+6=-6 | | X^3+16=43 | | 3sinx+2cosx=2 | | 25-5x=10-10x | | X^3+20=35.7 | | 6x+9=-51-4x | | Log(5)7+log(8)x=log(5)56 | | -2(8-x)-6=-12 | | Ln(2x+5)=1.4 | | 12xsquared-90x+150=0 | | X^3-12=-76 | | 15y^2=1-2y | | X^3+10=37 | | 3-6x=35 | | Y^2-y-20=-y-4 | | 2x+30=7x-25 | | 5x+1=1x+3 | | 15x-3(3x-1)=7(x-1) | | 5x+8=7x-16 | | 4x+49=104 | | x^2+2x+2ix+2i=0 | | 2x^3-14=2 | | w^2-4w=30+3w | | Y+19=38 | | 3x+5y-x+2y= | | Y+19=39 | | 64a^2=64 |

Equations solver categories