2-7n^2=-49

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

2-7n^2=-49

We move all terms to the left:

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

We add all the numbers together, and all the variables

-7n^2+51=0

a = -7; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-7)·51
Δ = 1428
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:

$\sqrt{\Delta}=\sqrt{1428}=\sqrt{4*357}=\sqrt{4}*\sqrt{357}=2\sqrt{357}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{357}}{2*-7}=\frac{0-2\sqrt{357}}{-14}
=-\frac{2\sqrt{357}}{-14}
=-\frac{\sqrt{357}}{-7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{357}}{2*-7}=\frac{0+2\sqrt{357}}{-14}
=\frac{2\sqrt{357}}{-14}
=\frac{\sqrt{357}}{-7}
$