n*n+5=84

Solution for n*n+5=84 equation:

n*n+5=84

We move all terms to the left:

n*n+5-(84)=0

We add all the numbers together, and all the variables

n*n-79=0

Wy multiply elements

n^2-79=0

a = 1; b = 0; c = -79;
Δ = b2-4ac
Δ = 02-4·1·(-79)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{79}}{2*1}=\frac{0-2\sqrt{79}}{2}
=-\frac{2\sqrt{79}}{2}
=-\sqrt{79}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{79}}{2*1}=\frac{0+2\sqrt{79}}{2}
=\frac{2\sqrt{79}}{2}
=\sqrt{79}
$