F(x)=-9x^2+18x-2

Solution for F(x)=-9x^2+18x-2 equation:

(F)=-9F^2+18F-2

We move all terms to the left:

(F)-(-9F^2+18F-2)=0

We get rid of parentheses

9F^2-18F+F+2=0

We add all the numbers together, and all the variables

9F^2-17F+2=0

a = 9; b = -17; c = +2;
Δ = b2-4ac
Δ = -172-4·9·2
Δ = 217
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{-(-17)-\sqrt{217}}{2*9}=\frac{17-\sqrt{217}}{18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{217}}{2*9}=\frac{17+\sqrt{217}}{18}
$