F(1)=4,f(2)=12,f(4)=46

Solution for F(1)=4,f(2)=12,f(4)=46 equation:

(1)=4.F(2)=12.F(4)=46

We move all terms to the left:

(1)-(4.F(2))=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-4.F^2+1=0

We add all the numbers together, and all the variables

-4F^2+1=0

a = -4; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-4)·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-4}=\frac{-4}{-8}
=1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-4}=\frac{4}{-8}
=-1/2
$