n2=114

Solution for n2=114 equation:

n2=114

We move all terms to the left:

n2-(114)=0

We add all the numbers together, and all the variables

n^2-114=0

a = 1; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·1·(-114)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{114}}{2*1}=\frac{0-2\sqrt{114}}{2}
=-\frac{2\sqrt{114}}{2}
=-\sqrt{114}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{114}}{2*1}=\frac{0+2\sqrt{114}}{2}
=\frac{2\sqrt{114}}{2}
=\sqrt{114}
$