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+33x+84=0

a = 3; b = 33; c = +84;
Δ = b2-4ac
Δ = 332-4·3·84
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-9}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+9}{2*3}=\frac{-24}{6}
=-4
$