100=n^2-54

Solution for 100=n^2-54 equation:

100=n^2-54

We move all terms to the left:

100-(n^2-54)=0

We get rid of parentheses

-n^2+54+100=0

We add all the numbers together, and all the variables

-1n^2+154=0

a = -1; b = 0; c = +154;
Δ = b2-4ac
Δ = 02-4·(-1)·154
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{154}}{2*-1}=\frac{0-2\sqrt{154}}{-2}
=-\frac{2\sqrt{154}}{-2}
=-\frac{\sqrt{154}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{154}}{2*-1}=\frac{0+2\sqrt{154}}{-2}
=\frac{2\sqrt{154}}{-2}
=\frac{\sqrt{154}}{-1}
$