F(x)=1/8x+2

Solution for F(x)=1/8x+2 equation:

(F)=1/8F+2

We move all terms to the left:

(F)-(1/8F+2)=0


Domain of the equation: 8F+2)!=0

F∈R


We get rid of parentheses

F-1/8F-2=0

We multiply all the terms by the denominator


F*8F-2*8F-1=0

Wy multiply elements

8F^2-16F-1=0

a = 8; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·8·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*8}=\frac{16-12\sqrt{2}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*8}=\frac{16+12\sqrt{2}}{16}
$