f(2)=3(2)^2-2(2)

Solution for f(2)=3(2)^2-2(2) equation:

f(2)=3(2)^2-2(2)

We move all terms to the left:

f(2)-(3(2)^2-2(2))=0

We add all the numbers together, and all the variables

f^2-1002=0

a = 1; b = 0; c = -1002;
Δ = b2-4ac
Δ = 02-4·1·(-1002)
Δ = 4008
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:

$\sqrt{\Delta}=\sqrt{4008}=\sqrt{4*1002}=\sqrt{4}*\sqrt{1002}=2\sqrt{1002}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1002}}{2*1}=\frac{0-2\sqrt{1002}}{2}
=-\frac{2\sqrt{1002}}{2}
=-\sqrt{1002}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1002}}{2*1}=\frac{0+2\sqrt{1002}}{2}
=\frac{2\sqrt{1002}}{2}
=\sqrt{1002}
$