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

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

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

We multiply parentheses ..

(+36x^2+27x-12x-9)=0

We get rid of parentheses

36x^2+27x-12x-9=0

We add all the numbers together, and all the variables

36x^2+15x-9=0

a = 36; b = 15; c = -9;
Δ = b2-4ac
Δ = 152-4·36·(-9)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-39}{2*36}=\frac{-54}{72}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+39}{2*36}=\frac{24}{72}
=1/3
$