f(2)=500(1.03)^2

Solution for f(2)=500(1.03)^2 equation:

f(2)=500(1.03)^2

We move all terms to the left:

f(2)-(500(1.03)^2)=0

We add all the numbers together, and all the variables

f^2-530.45=0

a = 1; b = 0; c = -530.45;
Δ = b2-4ac
Δ = 02-4·1·(-530.45)
Δ = 2121.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{2121.8}}{2*1}=\frac{0-\sqrt{2121.8}}{2}
=-\frac{\sqrt{}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{2121.8}}{2*1}=\frac{0+\sqrt{2121.8}}{2}
=\frac{\sqrt{}}{2}
$