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

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

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

We multiply parentheses ..

(+6x^2-2x-27x+9)=0

We get rid of parentheses

6x^2-2x-27x+9=0

We add all the numbers together, and all the variables

6x^2-29x+9=0

a = 6; b = -29; c = +9;
Δ = b2-4ac
Δ = -292-4·6·9
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-25}{2*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+25}{2*6}=\frac{54}{12}
=4+1/2
$