q^2=166

Solution for q^2=166 equation:

q^2=166

We move all terms to the left:

q^2-(166)=0

a = 1; b = 0; c = -166;
Δ = b2-4ac
Δ = 02-4·1·(-166)
Δ = 664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{166}}{2*1}=\frac{0-2\sqrt{166}}{2}
=-\frac{2\sqrt{166}}{2}
=-\sqrt{166}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{166}}{2*1}=\frac{0+2\sqrt{166}}{2}
=\frac{2\sqrt{166}}{2}
=\sqrt{166}
$