F(3)=x2+9x

Solution for F(3)=x2+9x equation:

(3)=F2+9F

We move all terms to the left:

(3)-(F2+9F)=0

We add all the numbers together, and all the variables

-(+F^2+9F)+3=0

We get rid of parentheses

-F^2-9F+3=0

We add all the numbers together, and all the variables

-1F^2-9F+3=0

a = -1; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-1)·3
Δ = 93
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{-(-9)-\sqrt{93}}{2*-1}=\frac{9-\sqrt{93}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{93}}{2*-1}=\frac{9+\sqrt{93}}{-2}
$