(9x+6)(8x-9)=0

Solution for (9x+6)(8x-9)=0 equation:

(9x+6)(8x-9)=0

We multiply parentheses ..

(+72x^2-81x+48x-54)=0

We get rid of parentheses

72x^2-81x+48x-54=0

We add all the numbers together, and all the variables

72x^2-33x-54=0

a = 72; b = -33; c = -54;
Δ = b2-4ac
Δ = -332-4·72·(-54)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-129}{2*72}=\frac{-96}{144}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+129}{2*72}=\frac{162}{144}
=1+1/8
$