b^2=171

Solution for b^2=171 equation:

b^2=171

We move all terms to the left:

b^2-(171)=0

a = 1; b = 0; c = -171;
Δ = b2-4ac
Δ = 02-4·1·(-171)
Δ = 684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*1}=\frac{0-6\sqrt{19}}{2}
=-\frac{6\sqrt{19}}{2}
=-3\sqrt{19}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*1}=\frac{0+6\sqrt{19}}{2}
=\frac{6\sqrt{19}}{2}
=3\sqrt{19}
$