x(x+2)-13(x+2)=0

Solution for x(x+2)-13(x+2)=0 equation:

x(x+2)-13(x+2)=0

We multiply parentheses

x^2+2x-13x-26=0

We add all the numbers together, and all the variables

x^2-11x-26=0

a = 1; b = -11; c = -26;
Δ = b2-4ac
Δ = -112-4·1·(-26)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-15}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+15}{2*1}=\frac{26}{2}
=13
$