10x(x-5)=0

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

10x(x-5)=0

We multiply parentheses

10x^2-50x=0

a = 10; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·10·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*10}=\frac{100}{20}
=5
$