7n^2+14n-57=-6

Solution for 7n^2+14n-57=-6 equation:

7n^2+14n-57=-6

We move all terms to the left:

7n^2+14n-57-(-6)=0

We add all the numbers together, and all the variables

7n^2+14n-51=0

a = 7; b = 14; c = -51;
Δ = b2-4ac
Δ = 142-4·7·(-51)
Δ = 1624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1624}=\sqrt{4*406}=\sqrt{4}*\sqrt{406}=2\sqrt{406}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{406}}{2*7}=\frac{-14-2\sqrt{406}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{406}}{2*7}=\frac{-14+2\sqrt{406}}{14}
$