F(x)=-4x2+6

Solution for F(x)=-4x2+6 equation:

(F)=-4F^2+6

We move all terms to the left:

(F)-(-4F^2+6)=0

We get rid of parentheses

4F^2+F-6=0

a = 4; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·4·(-6)
Δ = 97
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{97}}{2*4}=\frac{-1-\sqrt{97}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*4}=\frac{-1+\sqrt{97}}{8}
$