7n^2+14n-76=-3

Solution for 7n^2+14n-76=-3 equation:

7n^2+14n-76=-3

We move all terms to the left:

7n^2+14n-76-(-3)=0

We add all the numbers together, and all the variables

7n^2+14n-73=0

a = 7; b = 14; c = -73;
Δ = b2-4ac
Δ = 142-4·7·(-73)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{35}}{2*7}=\frac{-14-8\sqrt{35}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{35}}{2*7}=\frac{-14+8\sqrt{35}}{14}
$