6n^2+44n=-14

Solution for 6n^2+44n=-14 equation:

6n^2+44n=-14

We move all terms to the left:

6n^2+44n-(-14)=0

We add all the numbers together, and all the variables

6n^2+44n+14=0

a = 6; b = 44; c = +14;
Δ = b2-4ac
Δ = 442-4·6·14
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-40}{2*6}=\frac{-84}{12}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+40}{2*6}=\frac{-4}{12}
=-1/3
$