-3(x-7)(x+1)=0

Solution for -3(x-7)(x+1)=0 equation:

-3(x-7)(x+1)=0

We multiply parentheses ..

-3(+x^2+x-7x-7)=0

We multiply parentheses

-3x^2-3x+21x+21=0

We add all the numbers together, and all the variables

-3x^2+18x+21=0

a = -3; b = 18; c = +21;
Δ = b2-4ac
Δ = 182-4·(-3)·21
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-24}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+24}{2*-3}=\frac{6}{-6}
=-1
$