(5a-3)(3a+4)=0

Solution for (5a-3)(3a+4)=0 equation:

(5a-3)(3a+4)=0

We multiply parentheses ..

(+15a^2+20a-9a-12)=0

We get rid of parentheses

15a^2+20a-9a-12=0

We add all the numbers together, and all the variables

15a^2+11a-12=0

a = 15; b = 11; c = -12;
Δ = b2-4ac
Δ = 112-4·15·(-12)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*15}=\frac{-40}{30}
=-1+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*15}=\frac{18}{30}
=3/5
$