(9x-1)(3x+8)=0

Solution for (9x-1)(3x+8)=0 equation:

(9x-1)(3x+8)=0

We multiply parentheses ..

(+27x^2+72x-3x-8)=0

We get rid of parentheses

27x^2+72x-3x-8=0

We add all the numbers together, and all the variables

27x^2+69x-8=0

a = 27; b = 69; c = -8;
Δ = b2-4ac
Δ = 692-4·27·(-8)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-75}{2*27}=\frac{-144}{54}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+75}{2*27}=\frac{6}{54}
=1/9
$