n^2=89

Solution for n^2=89 equation:

n^2=89

We move all terms to the left:

n^2-(89)=0

a = 1; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·1·(-89)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{89}}{2*1}=\frac{0-2\sqrt{89}}{2}
=-\frac{2\sqrt{89}}{2}
=-\sqrt{89}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{89}}{2*1}=\frac{0+2\sqrt{89}}{2}
=\frac{2\sqrt{89}}{2}
=\sqrt{89}
$