x(x-10)+5(x-10)=0

Solution for x(x-10)+5(x-10)=0 equation:

x(x-10)+5(x-10)=0

We multiply parentheses

x^2-10x+5x-50=0

We add all the numbers together, and all the variables

x^2-5x-50=0

a = 1; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·1·(-50)
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{-(-5)-15}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*1}=\frac{20}{2}
=10
$