F(x)=2x2+4x-1

Solution for F(x)=2x2+4x-1 equation:

(F)=2F^2+4F-1

We move all terms to the left:

(F)-(2F^2+4F-1)=0

We get rid of parentheses

-2F^2+F-4F+1=0

We add all the numbers together, and all the variables

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

a = -2; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-2)·1
Δ = 17
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{-(-3)-\sqrt{17}}{2*-2}=\frac{3-\sqrt{17}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*-2}=\frac{3+\sqrt{17}}{-4}
$