(15-x)(18-x)=180

Solution for (15-x)(18-x)=180 equation:

(15-x)(18-x)=180

We move all terms to the left:

(15-x)(18-x)-(180)=0

We add all the numbers together, and all the variables

(-1x+15)(-1x+18)-180=0

We multiply parentheses ..

(+x^2-18x-15x+270)-180=0

We get rid of parentheses

x^2-18x-15x+270-180=0

We add all the numbers together, and all the variables

x^2-33x+90=0

a = 1; b = -33; c = +90;
Δ = b2-4ac
Δ = -332-4·1·90
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-27}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+27}{2*1}=\frac{60}{2}
=30
$