x^2+24x+68=180

Solution for x^2+24x+68=180 equation:

x^2+24x+68=180

We move all terms to the left:

x^2+24x+68-(180)=0

We add all the numbers together, and all the variables

x^2+24x-112=0

a = 1; b = 24; c = -112;
Δ = b2-4ac
Δ = 242-4·1·(-112)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-32}{2*1}=\frac{-56}{2}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+32}{2*1}=\frac{8}{2}
=4
$