(2x-5)(-3x-6)=0

Solution for (2x-5)(-3x-6)=0 equation:

(2x-5)(-3x-6)=0

We multiply parentheses ..

(-6x^2-12x+15x+30)=0

We get rid of parentheses

-6x^2-12x+15x+30=0

We add all the numbers together, and all the variables

-6x^2+3x+30=0

a = -6; b = 3; c = +30;
Δ = b2-4ac
Δ = 32-4·(-6)·30
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*-6}=\frac{24}{-12}
=-2
$