(15+x)(x+5)=231

Solution for (15+x)(x+5)=231 equation:

(15+x)(x+5)=231

We move all terms to the left:

(15+x)(x+5)-(231)=0

We add all the numbers together, and all the variables

(x+15)(x+5)-231=0

We multiply parentheses ..

(+x^2+5x+15x+75)-231=0

We get rid of parentheses

x^2+5x+15x+75-231=0

We add all the numbers together, and all the variables

x^2+20x-156=0

a = 1; b = 20; c = -156;
Δ = b2-4ac
Δ = 202-4·1·(-156)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-32}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+32}{2*1}=\frac{12}{2}
=6
$