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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2-33x-45=0

a = -6; b = -33; c = -45;
Δ = b2-4ac
Δ = -332-4·(-6)·(-45)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*-6}=\frac{30}{-12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*-6}=\frac{36}{-12}
=-3
$