(3x-2)(5x-2)=0

Solution for (3x-2)(5x-2)=0 equation:

(3x-2)(5x-2)=0

We multiply parentheses ..

(+15x^2-6x-10x+4)=0

We get rid of parentheses

15x^2-6x-10x+4=0

We add all the numbers together, and all the variables

15x^2-16x+4=0

a = 15; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·15·4
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*15}=\frac{12}{30}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*15}=\frac{20}{30}
=2/3
$