F(2)=9x^2-4x

Solution for F(2)=9x^2-4x equation:

(2)=9F^2-4F

We move all terms to the left:

(2)-(9F^2-4F)=0

We get rid of parentheses

-9F^2+4F+2=0

a = -9; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-9)·2
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{22}}{2*-9}=\frac{-4-2\sqrt{22}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{22}}{2*-9}=\frac{-4+2\sqrt{22}}{-18}
$