7n^2+16n=-4

Solution for 7n^2+16n=-4 equation:

7n^2+16n=-4

We move all terms to the left:

7n^2+16n-(-4)=0

We add all the numbers together, and all the variables

7n^2+16n+4=0

a = 7; b = 16; c = +4;
Δ = b2-4ac
Δ = 162-4·7·4
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12}{2*7}=\frac{-28}{14}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12}{2*7}=\frac{-4}{14}
=-2/7
$