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

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

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

We multiply parentheses ..

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

We multiply parentheses

-5x^2-15x+10x+30=0

We add all the numbers together, and all the variables

-5x^2-5x+30=0

a = -5; b = -5; c = +30;
Δ = b2-4ac
Δ = -52-4·(-5)·30
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*-5}=\frac{30}{-10}
=-3
$