(9x+5)(3x-16)=0

Solution for (9x+5)(3x-16)=0 equation:

(9x+5)(3x-16)=0

We multiply parentheses ..

(+27x^2-144x+15x-80)=0

We get rid of parentheses

27x^2-144x+15x-80=0

We add all the numbers together, and all the variables

27x^2-129x-80=0

a = 27; b = -129; c = -80;
Δ = b2-4ac
Δ = -1292-4·27·(-80)
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-129)-159}{2*27}=\frac{-30}{54}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+159}{2*27}=\frac{288}{54}
=5+1/3
$