f^2=197

Solution for f^2=197 equation:

f^2=197

We move all terms to the left:

f^2-(197)=0

a = 1; b = 0; c = -197;
Δ = b2-4ac
Δ = 02-4·1·(-197)
Δ = 788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{788}=\sqrt{4*197}=\sqrt{4}*\sqrt{197}=2\sqrt{197}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{197}}{2*1}=\frac{0-2\sqrt{197}}{2}
=-\frac{2\sqrt{197}}{2}
=-\sqrt{197}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{197}}{2*1}=\frac{0+2\sqrt{197}}{2}
=\frac{2\sqrt{197}}{2}
=\sqrt{197}
$