78=n*n-3

Solution for 78=n*n-3 equation:

78=n*n-3

We move all terms to the left:

78-(n*n-3)=0

We get rid of parentheses

-n*n+3+78=0

We add all the numbers together, and all the variables

-n*n+81=0

Wy multiply elements

-1n^2+81=0

a = -1; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-1)·81
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*-1}=\frac{-18}{-2}
=+9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*-1}=\frac{18}{-2}
=-9
$