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

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

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

We multiply parentheses ..

(+72x^2-40x+27x-15)=0

We get rid of parentheses

72x^2-40x+27x-15=0

We add all the numbers together, and all the variables

72x^2-13x-15=0

a = 72; b = -13; c = -15;
Δ = b2-4ac
Δ = -132-4·72·(-15)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-67}{2*72}=\frac{-54}{144}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+67}{2*72}=\frac{80}{144}
=5/9
$