3(x+7)(4x+1)=0

Solution for 3(x+7)(4x+1)=0 equation:

3(x+7)(4x+1)=0

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

12x^2+87x+21=0

a = 12; b = 87; c = +21;
Δ = b2-4ac
Δ = 872-4·12·21
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-81}{2*12}=\frac{-168}{24}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+81}{2*12}=\frac{-6}{24}
=-1/4
$