(8x-4)(9x+6)=0

Solution for (8x-4)(9x+6)=0 equation:

(8x-4)(9x+6)=0

We multiply parentheses ..

(+72x^2+48x-36x-24)=0

We get rid of parentheses

72x^2+48x-36x-24=0

We add all the numbers together, and all the variables

72x^2+12x-24=0

a = 72; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·72·(-24)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-84}{2*72}=\frac{-96}{144}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+84}{2*72}=\frac{72}{144}
=1/2
$