F(x)=1/8x+5

Solution for F(x)=1/8x+5 equation:

(F)=1/8F+5

We move all terms to the left:

(F)-(1/8F+5)=0


Domain of the equation: 8F+5)!=0

F∈R


We get rid of parentheses

F-1/8F-5=0

We multiply all the terms by the denominator


F*8F-5*8F-1=0

Wy multiply elements

8F^2-40F-1=0

a = 8; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·8·(-1)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{102}}{2*8}=\frac{40-4\sqrt{102}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{102}}{2*8}=\frac{40+4\sqrt{102}}{16}
$