6n^2+42n=-72

Solution for 6n^2+42n=-72 equation:

6n^2+42n=-72

We move all terms to the left:

6n^2+42n-(-72)=0

We add all the numbers together, and all the variables

6n^2+42n+72=0

a = 6; b = 42; c = +72;
Δ = b2-4ac
Δ = 422-4·6·72
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6}{2*6}=\frac{-48}{12}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6}{2*6}=\frac{-36}{12}
=-3
$