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