F(26)=x^2+3x+8

Solution for F(26)=x^2+3x+8 equation:

(26)=F^2+3F+8

We move all terms to the left:

(26)-(F^2+3F+8)=0

We get rid of parentheses

-F^2-3F-8+26=0

We add all the numbers together, and all the variables

-1F^2-3F+18=0

a = -1; b = -3; c = +18;
Δ = b2-4ac
Δ = -32-4·(-1)·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*-1}=\frac{-6}{-2}
=+3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-1}=\frac{12}{-2}
=-6
$