F(x)=2x^2-11+9

Solution for F(x)=2x^2-11+9 equation:

(F)=2F^2-11+9

We move all terms to the left:

(F)-(2F^2-11+9)=0

We get rid of parentheses

-2F^2+F+11-9=0

We add all the numbers together, and all the variables

-2F^2+F+2=0

a = -2; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-2)·2
Δ = 17
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{-(1)-\sqrt{17}}{2*-2}=\frac{-1-\sqrt{17}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-2}=\frac{-1+\sqrt{17}}{-4}
$