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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-2)·9
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*-2}=\frac{-2-2\sqrt{19}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*-2}=\frac{-2+2\sqrt{19}}{-4}
$