-3x(x-8)+6x=-2x-4(x+6)

Solution for -3x(x-8)+6x=-2x-4(x+6) equation:

-3x(x-8)+6x=-2x-4(x+6)

We move all terms to the left:

-3x(x-8)+6x-(-2x-4(x+6))=0

We add all the numbers together, and all the variables

6x-3x(x-8)-(-2x-4(x+6))=0

We multiply parentheses

-3x^2+6x+24x-(-2x-4(x+6))=0


We calculate terms in parentheses: -(-2x-4(x+6)), so:

-2x-4(x+6)

We multiply parentheses

-2x-4x-24

We add all the numbers together, and all the variables

-6x-24

Back to the equation:

-(-6x-24)


We add all the numbers together, and all the variables

-3x^2+30x-(-6x-24)=0

We get rid of parentheses

-3x^2+30x+6x+24=0

We add all the numbers together, and all the variables

-3x^2+36x+24=0

a = -3; b = 36; c = +24;
Δ = b2-4ac
Δ = 362-4·(-3)·24
Δ = 1584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{11}}{2*-3}=\frac{-36-12\sqrt{11}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{11}}{2*-3}=\frac{-36+12\sqrt{11}}{-6}
$