68+x(x-24)=180

Solution for 68+x(x-24)=180 equation:

68+x(x-24)=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x-24)-112=0

We multiply parentheses

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