(15+x)(x+15)=231

Solution for (15+x)(x+15)=231 equation:

(15+x)(x+15)=231

We move all terms to the left:

(15+x)(x+15)-(231)=0

We add all the numbers together, and all the variables

(x+15)(x+15)-231=0

We multiply parentheses ..

(+x^2+15x+15x+225)-231=0

We get rid of parentheses

x^2+15x+15x+225-231=0

We add all the numbers together, and all the variables

x^2+30x-6=0

a = 1; b = 30; c = -6;
Δ = b2-4ac
Δ = 302-4·1·(-6)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*1}=\frac{-30-2\sqrt{231}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*1}=\frac{-30+2\sqrt{231}}{2}
$