F(2)=2x^2+5x-9

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

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

We move all terms to the left:

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

We get rid of parentheses

-2F^2-5F+9+2=0

We add all the numbers together, and all the variables

-2F^2-5F+11=0

a = -2; b = -5; c = +11;
Δ = b2-4ac
Δ = -52-4·(-2)·11
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{113}}{2*-2}=\frac{5-\sqrt{113}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{113}}{2*-2}=\frac{5+\sqrt{113}}{-4}
$