(5x-1)(3x-1)=0

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

(5x-1)(3x-1)=0

We multiply parentheses ..

(+15x^2-5x-3x+1)=0

We get rid of parentheses

15x^2-5x-3x+1=0

We add all the numbers together, and all the variables

15x^2-8x+1=0

a = 15; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·15·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*15}=\frac{6}{30}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*15}=\frac{10}{30}
=1/3
$