n^2-3=49

Solution for n^2-3=49 equation:

n^2-3=49

We move all terms to the left:

n^2-3-(49)=0

We add all the numbers together, and all the variables

n^2-52=0

a = 1; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·1·(-52)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*1}=\frac{0-4\sqrt{13}}{2}
=-\frac{4\sqrt{13}}{2}
=-2\sqrt{13}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*1}=\frac{0+4\sqrt{13}}{2}
=\frac{4\sqrt{13}}{2}
=2\sqrt{13}
$