(5a-2)(8a-3)=0

Solution for (5a-2)(8a-3)=0 equation:

(5a-2)(8a-3)=0

We multiply parentheses ..

(+40a^2-15a-16a+6)=0

We get rid of parentheses

40a^2-15a-16a+6=0

We add all the numbers together, and all the variables

40a^2-31a+6=0

a = 40; b = -31; c = +6;
Δ = b2-4ac
Δ = -312-4·40·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-1}{2*40}=\frac{30}{80}
=3/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+1}{2*40}=\frac{32}{80}
=2/5
$