3(x+4)(x-7)=0

Solution for 3(x+4)(x-7)=0 equation:

3(x+4)(x-7)=0

We multiply parentheses ..

3(+x^2-7x+4x-28)=0

We multiply parentheses

3x^2-21x+12x-84=0

We add all the numbers together, and all the variables

3x^2-9x-84=0

a = 3; b = -9; c = -84;
Δ = b2-4ac
Δ = -92-4·3·(-84)
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{-(-9)-33}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*3}=\frac{42}{6}
=7
$