(9x-3)(2x+9)=0

Solution for (9x-3)(2x+9)=0 equation:

(9x-3)(2x+9)=0

We multiply parentheses ..

(+18x^2+81x-6x-27)=0

We get rid of parentheses

18x^2+81x-6x-27=0

We add all the numbers together, and all the variables

18x^2+75x-27=0

a = 18; b = 75; c = -27;
Δ = b2-4ac
Δ = 752-4·18·(-27)
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-87}{2*18}=\frac{-162}{36}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+87}{2*18}=\frac{12}{36}
=1/3
$