144=f^2

Solution for 144=f^2 equation:

144=f^2

We move all terms to the left:

144-(f^2)=0

We add all the numbers together, and all the variables

-1f^2+144=0

a = -1; b = 0; c = +144;
Δ = b2-4ac
Δ = 02-4·(-1)·144
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-1}=\frac{-24}{-2}
=+12
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-1}=\frac{24}{-2}
=-12
$