(6a-5)(3a-8)=0

Solution for (6a-5)(3a-8)=0 equation:

(6a-5)(3a-8)=0

We multiply parentheses ..

(+18a^2-48a-15a+40)=0

We get rid of parentheses

18a^2-48a-15a+40=0

We add all the numbers together, and all the variables

18a^2-63a+40=0

a = 18; b = -63; c = +40;
Δ = b2-4ac
Δ = -632-4·18·40
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-33}{2*18}=\frac{30}{36}
=5/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+33}{2*18}=\frac{96}{36}
=2+2/3
$