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

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

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

We multiply parentheses ..

(+40a^2-24a+15a-9)=0

We get rid of parentheses

40a^2-24a+15a-9=0

We add all the numbers together, and all the variables

40a^2-9a-9=0

a = 40; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·40·(-9)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*40}=\frac{-30}{80}
=-3/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*40}=\frac{48}{80}
=3/5
$