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

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

(X-9)(3X+8)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3X^2-19X-72=0

a = 3; b = -19; c = -72;
Δ = b2-4ac
Δ = -192-4·3·(-72)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-35}{2*3}=\frac{-16}{6}
=-2+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+35}{2*3}=\frac{54}{6}
=9
$