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

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

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

We multiply parentheses ..

(+6x^2-15x+18x-45)=0

We get rid of parentheses

6x^2-15x+18x-45=0

We add all the numbers together, and all the variables

6x^2+3x-45=0

a = 6; b = 3; c = -45;
Δ = b2-4ac
Δ = 32-4·6·(-45)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-33}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+33}{2*6}=\frac{30}{12}
=2+1/2
$