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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-6x(x+4)+3x-(-1x+8)=0

We add all the numbers together, and all the variables

3x-6x(x+4)-(-1x+8)=0

We multiply parentheses

-6x^2+3x-24x-(-1x+8)=0

We get rid of parentheses

-6x^2+3x-24x+1x-8=0

We add all the numbers together, and all the variables

-6x^2-20x-8=0

a = -6; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·(-6)·(-8)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{13}}{2*-6}=\frac{20-4\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{13}}{2*-6}=\frac{20+4\sqrt{13}}{-12}
$