(15+x)(9+x)=270

Solution for (15+x)(9+x)=270 equation:

(15+x)(9+x)=270

We move all terms to the left:

(15+x)(9+x)-(270)=0

We add all the numbers together, and all the variables

(x+15)(x+9)-270=0

We multiply parentheses ..

(+x^2+9x+15x+135)-270=0

We get rid of parentheses

x^2+9x+15x+135-270=0

We add all the numbers together, and all the variables

x^2+24x-135=0

a = 1; b = 24; c = -135;
Δ = b2-4ac
Δ = 242-4·1·(-135)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{31}}{2*1}=\frac{-24-6\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{31}}{2*1}=\frac{-24+6\sqrt{31}}{2}
$