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

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

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

We multiply parentheses ..

(+10a^2-15a-16a+24)=0

We get rid of parentheses

10a^2-15a-16a+24=0

We add all the numbers together, and all the variables

10a^2-31a+24=0

a = 10; b = -31; c = +24;
Δ = b2-4ac
Δ = -312-4·10·24
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*10}=\frac{30}{20}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+1}{2*10}=\frac{32}{20}
=1+3/5
$