(12+x)(10+x)=180

Solution for (12+x)(10+x)=180 equation:

(12+x)(10+x)=180

We move all terms to the left:

(12+x)(10+x)-(180)=0

We add all the numbers together, and all the variables

(x+12)(x+10)-180=0

We multiply parentheses ..

(+x^2+10x+12x+120)-180=0

We get rid of parentheses

x^2+10x+12x+120-180=0

We add all the numbers together, and all the variables

x^2+22x-60=0

a = 1; b = 22; c = -60;
Δ = b2-4ac
Δ = 222-4·1·(-60)
Δ = 724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{181}}{2*1}=\frac{-22-2\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{181}}{2*1}=\frac{-22+2\sqrt{181}}{2}
$