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

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

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

We multiply parentheses ..

(+72x^2+54x-64x-48)=0

We get rid of parentheses

72x^2+54x-64x-48=0

We add all the numbers together, and all the variables

72x^2-10x-48=0

a = 72; b = -10; c = -48;
Δ = b2-4ac
Δ = -102-4·72·(-48)
Δ = 13924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13924}=118$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-118}{2*72}=\frac{-108}{144}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+118}{2*72}=\frac{128}{144}
=8/9
$