f(2)=2(2)^2+5(2)-9

Solution for f(2)=2(2)^2+5(2)-9 equation:

f(2)=2(2)^2+5(2)-9

We move all terms to the left:

f(2)-(2(2)^2+5(2)-9)=0

We add all the numbers together, and all the variables

f^2-527=0

a = 1; b = 0; c = -527;
Δ = b2-4ac
Δ = 02-4·1·(-527)
Δ = 2108
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:

$\sqrt{\Delta}=\sqrt{2108}=\sqrt{4*527}=\sqrt{4}*\sqrt{527}=2\sqrt{527}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{527}}{2*1}=\frac{0-2\sqrt{527}}{2}
=-\frac{2\sqrt{527}}{2}
=-\sqrt{527}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{527}}{2*1}=\frac{0+2\sqrt{527}}{2}
=\frac{2\sqrt{527}}{2}
=\sqrt{527}
$