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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-12x^2-36x-15=0

a = -12; b = -36; c = -15;
Δ = b2-4ac
Δ = -362-4·(-12)·(-15)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24}{2*-12}=\frac{12}{-24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24}{2*-12}=\frac{60}{-24}
=-2+1/2
$