F(x)=x^2+14x+8

Solution for F(x)=x^2+14x+8 equation:

(F)=F^2+14F+8

We move all terms to the left:

(F)-(F^2+14F+8)=0

We get rid of parentheses

-F^2+F-14F-8=0

We add all the numbers together, and all the variables

-1F^2-13F-8=0

a = -1; b = -13; c = -8;
Δ = b2-4ac
Δ = -132-4·(-1)·(-8)
Δ = 137
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{-(-13)-\sqrt{137}}{2*-1}=\frac{13-\sqrt{137}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{137}}{2*-1}=\frac{13+\sqrt{137}}{-2}
$