(4x-9)(5x+4)=0

Solution for (4x-9)(5x+4)=0 equation:

(4x-9)(5x+4)=0

We multiply parentheses ..

(+20x^2+16x-45x-36)=0

We get rid of parentheses

20x^2+16x-45x-36=0

We add all the numbers together, and all the variables

20x^2-29x-36=0

a = 20; b = -29; c = -36;
Δ = b2-4ac
Δ = -292-4·20·(-36)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-61}{2*20}=\frac{-32}{40}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+61}{2*20}=\frac{90}{40}
=2+1/4
$