F(5)=3x^2+x-18

Solution for F(5)=3x^2+x-18 equation:

(5)=3F^2+F-18

We move all terms to the left:

(5)-(3F^2+F-18)=0

We get rid of parentheses

-3F^2-F+18+5=0

We add all the numbers together, and all the variables

-3F^2-1F+23=0

a = -3; b = -1; c = +23;
Δ = b2-4ac
Δ = -12-4·(-3)·23
Δ = 277
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{277}}{2*-3}=\frac{1-\sqrt{277}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{277}}{2*-3}=\frac{1+\sqrt{277}}{-6}
$