4x^2+32=-24x

Solution for 4x^2+32=-24x equation:

4x^2+32=-24x

We move all terms to the left:

4x^2+32-(-24x)=0

We get rid of parentheses

4x^2+24x+32=0

a = 4; b = 24; c = +32;
Δ = b2-4ac
Δ = 242-4·4·32
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8}{2*4}=\frac{-16}{8}
=-2
$