(4x-9)(5x+8)=0

Solution for (4x-9)(5x+8)=0 equation:

(4x-9)(5x+8)=0

We multiply parentheses ..

(+20x^2+32x-45x-72)=0

We get rid of parentheses

20x^2+32x-45x-72=0

We add all the numbers together, and all the variables

20x^2-13x-72=0

a = 20; b = -13; c = -72;
Δ = b2-4ac
Δ = -132-4·20·(-72)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-77}{2*20}=\frac{-64}{40}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+77}{2*20}=\frac{90}{40}
=2+1/4
$