x(15+x)=100

Solution for x(15+x)=100 equation:

x(15+x)=100

We move all terms to the left:

x(15+x)-(100)=0

We add all the numbers together, and all the variables

x(x+15)-100=0

We multiply parentheses

x^2+15x-100=0

a = 1; b = 15; c = -100;
Δ = b2-4ac
Δ = 152-4·1·(-100)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*1}=\frac{10}{2}
=5
$