f^2=55

Solution for f^2=55 equation:

f^2=55

We move all terms to the left:

f^2-(55)=0

a = 1; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·1·(-55)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{55}}{2*1}=\frac{0-2\sqrt{55}}{2}
=-\frac{2\sqrt{55}}{2}
=-\sqrt{55}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{55}}{2*1}=\frac{0+2\sqrt{55}}{2}
=\frac{2\sqrt{55}}{2}
=\sqrt{55}
$