5x*(3x-1)=0

Solution for 5x*(3x-1)=0 equation:

5x*(3x-1)=0

We multiply parentheses

15x^2-5x=0

a = 15; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·15·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*15}=\frac{10}{30}
=1/3
$