10x(x-50)=0

Solution for 10x(x-50)=0 equation:

10x(x-50)=0

We multiply parentheses

10x^2-500x=0

a = 10; b = -500; c = 0;
Δ = b2-4ac
Δ = -5002-4·10·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-500}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+500}{2*10}=\frac{1000}{20}
=50
$