(x+42)(x=52)=180

Solution for (x+42)(x=52)=180 equation:

(x+42)(x=52)=180

We move all terms to the left:

(x+42)(x-(52))=0

We multiply parentheses ..

(+x^2-52x+42x-2184)=0

We get rid of parentheses

x^2-52x+42x-2184=0

We add all the numbers together, and all the variables

x^2-10x-2184=0

a = 1; b = -10; c = -2184;
Δ = b2-4ac
Δ = -102-4·1·(-2184)
Δ = 8836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8836}=94$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-94}{2*1}=\frac{-84}{2}
=-42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+94}{2*1}=\frac{104}{2}
=52
$