F(x)=9-x2

Solution for F(x)=9-x2 equation:

(F)=9-F2

We move all terms to the left:

(F)-(9-F2)=0

We add all the numbers together, and all the variables

-(-1F^2+9)+F=0

We get rid of parentheses

1F^2+F-9=0

We add all the numbers together, and all the variables

F^2+F-9=0

a = 1; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·1·(-9)
Δ = 37
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{37}}{2*1}=\frac{-1-\sqrt{37}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*1}=\frac{-1+\sqrt{37}}{2}
$