F(x)=2x^2+12x+1

Solution for F(x)=2x^2+12x+1 equation:

(F)=2F^2+12F+1

We move all terms to the left:

(F)-(2F^2+12F+1)=0

We get rid of parentheses

-2F^2+F-12F-1=0

We add all the numbers together, and all the variables

-2F^2-11F-1=0

a = -2; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·(-2)·(-1)
Δ = 113
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{-(-11)-\sqrt{113}}{2*-2}=\frac{11-\sqrt{113}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{113}}{2*-2}=\frac{11+\sqrt{113}}{-4}
$