-8x+2x^2=24

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

-8x+2x^2=24

We move all terms to the left:

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