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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3a^2-17a+10=0

a = 3; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·3·10
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*3}=\frac{4}{6}
=2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*3}=\frac{30}{6}
=5
$