(2x-9)(3x+5)=0

Solution for (2x-9)(3x+5)=0 equation:

(2x-9)(3x+5)=0

We multiply parentheses ..

(+6x^2+10x-27x-45)=0

We get rid of parentheses

6x^2+10x-27x-45=0

We add all the numbers together, and all the variables

6x^2-17x-45=0

a = 6; b = -17; c = -45;
Δ = b2-4ac
Δ = -172-4·6·(-45)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-37}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+37}{2*6}=\frac{54}{12}
=4+1/2
$