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

We add all the numbers together, and all the variables

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