F(x)=1/8x+4

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

(F)=1/8F+4

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-1/8F-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

8F^2-32F-1=0

a = 8; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·8·(-1)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{66}}{2*8}=\frac{32-4\sqrt{66}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*8}=\frac{32+4\sqrt{66}}{16}
$