n^2+14n-49=-7

Solution for n^2+14n-49=-7 equation:

n^2+14n-49=-7

We move all terms to the left:

n^2+14n-49-(-7)=0

We add all the numbers together, and all the variables

n^2+14n-42=0

a = 1; b = 14; c = -42;
Δ = b2-4ac
Δ = 142-4·1·(-42)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{91}}{2*1}=\frac{-14-2\sqrt{91}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{91}}{2*1}=\frac{-14+2\sqrt{91}}{2}
$