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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2+3x+8x-(x-8)=0

We get rid of parentheses

-2x^2+3x+8x-x+8=0

We add all the numbers together, and all the variables

-2x^2+10x+8=0

a = -2; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·(-2)·8
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{41}}{2*-2}=\frac{-10-2\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{41}}{2*-2}=\frac{-10+2\sqrt{41}}{-4}
$