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

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

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

We multiply parentheses ..

(+15x^2-9x-10x+6)=0

We get rid of parentheses

15x^2-9x-10x+6=0

We add all the numbers together, and all the variables

15x^2-19x+6=0

a = 15; b = -19; c = +6;
Δ = b2-4ac
Δ = -192-4·15·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-1}{2*15}=\frac{18}{30}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+1}{2*15}=\frac{20}{30}
=2/3
$