12x+6x^2+42x=0

Solution for 12x+6x^2+42x=0 equation:

12x+6x^2+42x=0

We add all the numbers together, and all the variables

6x^2+54x=0

a = 6; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·6·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*6}=\frac{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*6}=\frac{0}{12}
=0
$