3(x-6)(x+1)=0

Solution for 3(x-6)(x+1)=0 equation:

3(x-6)(x+1)=0

We multiply parentheses ..

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

We multiply parentheses

3x^2+3x-18x-18=0

We add all the numbers together, and all the variables

3x^2-15x-18=0

a = 3; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·3·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*3}=\frac{36}{6}
=6
$