7n^2+57n=-56

Solution for 7n^2+57n=-56 equation:

7n^2+57n=-56

We move all terms to the left:

7n^2+57n-(-56)=0

We add all the numbers together, and all the variables

7n^2+57n+56=0

a = 7; b = 57; c = +56;
Δ = b2-4ac
Δ = 572-4·7·56
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-41}{2*7}=\frac{-98}{14}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+41}{2*7}=\frac{-16}{14}
=-1+1/7
$