f(2)=5(2)^2+9(2)-3

Solution for f(2)=5(2)^2+9(2)-3 equation:

f(2)=5(2)^2+9(2)-3

We move all terms to the left:

f(2)-(5(2)^2+9(2)-3)=0

We add all the numbers together, and all the variables

f^2-2793=0

a = 1; b = 0; c = -2793;
Δ = b2-4ac
Δ = 02-4·1·(-2793)
Δ = 11172
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:

$\sqrt{\Delta}=\sqrt{11172}=\sqrt{196*57}=\sqrt{196}*\sqrt{57}=14\sqrt{57}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{57}}{2*1}=\frac{0-14\sqrt{57}}{2}
=-\frac{14\sqrt{57}}{2}
=-7\sqrt{57}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{57}}{2*1}=\frac{0+14\sqrt{57}}{2}
=\frac{14\sqrt{57}}{2}
=7\sqrt{57}
$