4x-8x^2-8x=-24

Solution for 4x-8x^2-8x=-24 equation:

4x-8x^2-8x=-24

We move all terms to the left:

4x-8x^2-8x-(-24)=0

We add all the numbers together, and all the variables

-8x^2-4x+24=0

a = -8; b = -4; c = +24;
Δ = b2-4ac
Δ = -42-4·(-8)·24
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*-8}=\frac{32}{-16}
=-2
$