(24+x)(15+x)=900

Solution for (24+x)(15+x)=900 equation:

(24+x)(15+x)=900

We move all terms to the left:

(24+x)(15+x)-(900)=0

We add all the numbers together, and all the variables

(x+24)(x+15)-900=0

We multiply parentheses ..

(+x^2+15x+24x+360)-900=0

We get rid of parentheses

x^2+15x+24x+360-900=0

We add all the numbers together, and all the variables

x^2+39x-540=0

a = 1; b = 39; c = -540;
Δ = b2-4ac
Δ = 392-4·1·(-540)
Δ = 3681
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:

$\sqrt{\Delta}=\sqrt{3681}=\sqrt{9*409}=\sqrt{9}*\sqrt{409}=3\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{409}}{2*1}=\frac{-39-3\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{409}}{2*1}=\frac{-39+3\sqrt{409}}{2}
$