x(x+15)=126

Solution for x(x+15)=126 equation:

x(x+15)=126

We move all terms to the left:

x(x+15)-(126)=0

We multiply parentheses

x^2+15x-126=0

a = 1; b = 15; c = -126;
Δ = b2-4ac
Δ = 152-4·1·(-126)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-27}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+27}{2*1}=\frac{12}{2}
=6
$