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

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

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

We multiply parentheses ..

(+32x^2-40x+36x-45)=0

We get rid of parentheses

32x^2-40x+36x-45=0

We add all the numbers together, and all the variables

32x^2-4x-45=0

a = 32; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·32·(-45)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-76}{2*32}=\frac{-72}{64}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+76}{2*32}=\frac{80}{64}
=1+1/4
$