48=8x^2-8x

Solution for 48=8x^2-8x equation:

48=8x^2-8x

We move all terms to the left:

48-(8x^2-8x)=0

We get rid of parentheses

-8x^2+8x+48=0

a = -8; b = 8; c = +48;
Δ = b2-4ac
Δ = 82-4·(-8)·48
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-40}{2*-8}=\frac{-48}{-16}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+40}{2*-8}=\frac{32}{-16}
=-2
$