(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^2-25x-9=0

a = 6; b = -25; c = -9;
Δ = b2-4ac
Δ = -252-4·6·(-9)
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*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+29}{2*6}=\frac{54}{12}
=4+1/2
$