f(2)=9(2)^2-4(2)

Solution for f(2)=9(2)^2-4(2) equation:

f(2)=9(2)^2-4(2)

We move all terms to the left:

f(2)-(9(2)^2-4(2))=0

We add all the numbers together, and all the variables

f^2-8422=0

a = 1; b = 0; c = -8422;
Δ = b2-4ac
Δ = 02-4·1·(-8422)
Δ = 33688
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:

$\sqrt{\Delta}=\sqrt{33688}=\sqrt{4*8422}=\sqrt{4}*\sqrt{8422}=2\sqrt{8422}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{8422}}{2*1}=\frac{0-2\sqrt{8422}}{2}
=-\frac{2\sqrt{8422}}{2}
=-\sqrt{8422}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{8422}}{2*1}=\frac{0+2\sqrt{8422}}{2}
=\frac{2\sqrt{8422}}{2}
=\sqrt{8422}
$