F(x)=1/4x+8

Solution for F(x)=1/4x+8 equation:

(F)=1/4F+8

We move all terms to the left:

(F)-(1/4F+8)=0


Domain of the equation: 4F+8)!=0

F∈R


We get rid of parentheses

F-1/4F-8=0

We multiply all the terms by the denominator


F*4F-8*4F-1=0

Wy multiply elements

4F^2-32F-1=0

a = 4; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·4·(-1)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{65}}{2*4}=\frac{32-4\sqrt{65}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{65}}{2*4}=\frac{32+4\sqrt{65}}{8}
$