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

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

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

We multiply parentheses ..

(+32x^2-72x+36x-81)=0

We get rid of parentheses

32x^2-72x+36x-81=0

We add all the numbers together, and all the variables

32x^2-36x-81=0

a = 32; b = -36; c = -81;
Δ = b2-4ac
Δ = -362-4·32·(-81)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-108}{2*32}=\frac{-72}{64}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+108}{2*32}=\frac{144}{64}
=2+1/4
$