3(x+1)(x-5)=0

Solution for 3(x+1)(x-5)=0 equation:

3(x+1)(x-5)=0

We multiply parentheses ..

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

We multiply parentheses

3x^2-15x+3x-15=0

We add all the numbers together, and all the variables

3x^2-12x-15=0

a = 3; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·3·(-15)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*3}=\frac{30}{6}
=5
$