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

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

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

We multiply parentheses ..

3(+x^2-6x+5x-30)=0

We multiply parentheses

3x^2-18x+15x-90=0

We add all the numbers together, and all the variables

3x^2-3x-90=0

a = 3; b = -3; c = -90;
Δ = b2-4ac
Δ = -32-4·3·(-90)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-33}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+33}{2*3}=\frac{36}{6}
=6
$