(13x-3)(15x-5)=0

Solution for (13x-3)(15x-5)=0 equation:

(13x-3)(15x-5)=0

We multiply parentheses ..

(+195x^2-65x-45x+15)=0

We get rid of parentheses

195x^2-65x-45x+15=0

We add all the numbers together, and all the variables

195x^2-110x+15=0

a = 195; b = -110; c = +15;
Δ = b2-4ac
Δ = -1102-4·195·15
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-20}{2*195}=\frac{90}{390}
=3/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+20}{2*195}=\frac{130}{390}
=1/3
$