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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2+12x+10x+120)), so:

(+x^2+12x+10x+120)

We get rid of parentheses

x^2+12x+10x+120

We add all the numbers together, and all the variables

x^2+22x+120

Back to the equation:

-(x^2+22x+120)


We get rid of parentheses

-x^2-22x-120+180=0

We add all the numbers together, and all the variables

-1x^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}
$