f(2)=2(2)^2+9(2)-1

Solution for f(2)=2(2)^2+9(2)-1 equation:

f(2)=2(2)^2+9(2)-1

We move all terms to the left:

f(2)-(2(2)^2+9(2)-1)=0

We add all the numbers together, and all the variables

f^2-575=0

a = 1; b = 0; c = -575;
Δ = b2-4ac
Δ = 02-4·1·(-575)
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{23}}{2*1}=\frac{0-10\sqrt{23}}{2}
=-\frac{10\sqrt{23}}{2}
=-5\sqrt{23}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{23}}{2*1}=\frac{0+10\sqrt{23}}{2}
=\frac{10\sqrt{23}}{2}
=5\sqrt{23}
$