(-3x+8)(9x-4)=0

Solution for (-3x+8)(9x-4)=0 equation:

(-3x+8)(9x-4)=0

We multiply parentheses ..

(-27x^2+12x+72x-32)=0

We get rid of parentheses

-27x^2+12x+72x-32=0

We add all the numbers together, and all the variables

-27x^2+84x-32=0

a = -27; b = 84; c = -32;
Δ = b2-4ac
Δ = 842-4·(-27)·(-32)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-60}{2*-27}=\frac{-144}{-54}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+60}{2*-27}=\frac{-24}{-54}
=4/9
$