12x(x-5)=0

Solution for 12x(x-5)=0 equation:

12x(x-5)=0

We multiply parentheses

12x^2-60x=0

a = 12; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·12·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*12}=\frac{120}{24}
=5
$