F(2)=x(2)+16(x)-46

Solution for F(2)=x(2)+16(x)-46 equation:

(2)=F(2)+16(F)-46

We move all terms to the left:

(2)-(F(2)+16(F)-46)=0

We add all the numbers together, and all the variables

-(+F^2+16F-46)+2=0

We get rid of parentheses

-F^2-16F+46+2=0

We add all the numbers together, and all the variables

-1F^2-16F+48=0

a = -1; b = -16; c = +48;
Δ = b2-4ac
Δ = -162-4·(-1)·48
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{7}}{2*-1}=\frac{16-8\sqrt{7}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{7}}{2*-1}=\frac{16+8\sqrt{7}}{-2}
$