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

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

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

We multiply parentheses ..

(+72x^2+18x-64x-16)=0

We get rid of parentheses

72x^2+18x-64x-16=0

We add all the numbers together, and all the variables

72x^2-46x-16=0

a = 72; b = -46; c = -16;
Δ = b2-4ac
Δ = -462-4·72·(-16)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-82}{2*72}=\frac{-36}{144}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+82}{2*72}=\frac{128}{144}
=8/9
$