(9x-1)(2x+3)=0

Solution for (9x-1)(2x+3)=0 equation:

(9x-1)(2x+3)=0

We multiply parentheses ..

(+18x^2+27x-2x-3)=0

We get rid of parentheses

18x^2+27x-2x-3=0

We add all the numbers together, and all the variables

18x^2+25x-3=0

a = 18; b = 25; c = -3;
Δ = b2-4ac
Δ = 252-4·18·(-3)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-29}{2*18}=\frac{-54}{36}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+29}{2*18}=\frac{4}{36}
=1/9
$