(3a+5)(8a-9)=0

Solution for (3a+5)(8a-9)=0 equation:

(3a+5)(8a-9)=0

We multiply parentheses ..

(+24a^2-27a+40a-45)=0

We get rid of parentheses

24a^2-27a+40a-45=0

We add all the numbers together, and all the variables

24a^2+13a-45=0

a = 24; b = 13; c = -45;
Δ = b2-4ac
Δ = 132-4·24·(-45)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-67}{2*24}=\frac{-80}{48}
=-1+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+67}{2*24}=\frac{54}{48}
=1+1/8
$