(15+x)(24+x)=540

Solution for (15+x)(24+x)=540 equation:

(15+x)(24+x)=540

We move all terms to the left:

(15+x)(24+x)-(540)=0

We add all the numbers together, and all the variables

(x+15)(x+24)-540=0

We multiply parentheses ..

(+x^2+24x+15x+360)-540=0

We get rid of parentheses

x^2+24x+15x+360-540=0

We add all the numbers together, and all the variables

x^2+39x-180=0

a = 1; b = 39; c = -180;
Δ = b2-4ac
Δ = 392-4·1·(-180)
Δ = 2241
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:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{249}}{2*1}=\frac{-39-3\sqrt{249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{249}}{2*1}=\frac{-39+3\sqrt{249}}{2}
$