-4x-32=x^2+2x-24

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

-4x-32=x^2+2x-24

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-6x-8=0

a = -1; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·(-1)·(-8)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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