(3a-2)(5a-1)=0

Solution for (3a-2)(5a-1)=0 equation:

(3a-2)(5a-1)=0

We multiply parentheses ..

(+15a^2-3a-10a+2)=0

We get rid of parentheses

15a^2-3a-10a+2=0

We add all the numbers together, and all the variables

15a^2-13a+2=0

a = 15; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·15·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*15}=\frac{6}{30}
=1/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*15}=\frac{20}{30}
=2/3
$