(8x-9)(2x+9)=0

Solution for (8x-9)(2x+9)=0 equation:

(8x-9)(2x+9)=0

We multiply parentheses ..

(+16x^2+72x-18x-81)=0

We get rid of parentheses

16x^2+72x-18x-81=0

We add all the numbers together, and all the variables

16x^2+54x-81=0

a = 16; b = 54; c = -81;
Δ = b2-4ac
Δ = 542-4·16·(-81)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-90}{2*16}=\frac{-144}{32}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+90}{2*16}=\frac{36}{32}
=1+1/8
$