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