F(x)=2x2-5=1

Solution for F(x)=2x2-5=1 equation:

(F)=2F^2-5=1

We move all terms to the left:

(F)-(2F^2-5)=0

We get rid of parentheses

-2F^2+F+5=0

a = -2; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-2)·5
Δ = 41
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{41}}{2*-2}=\frac{-1-\sqrt{41}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*-2}=\frac{-1+\sqrt{41}}{-4}
$