-2x^2+24=8x

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

-2x^2+24=8x

We move all terms to the left:

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

a = -2; b = -8; c = +24;
Δ = b2-4ac
Δ = -82-4·(-2)·24
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*-2}=\frac{24}{-4}
=-6
$