F(x+8)=1/4x+5

Solution for F(x+8)=1/4x+5 equation:

(F+8)=1/4F+5

We move all terms to the left:

(F+8)-(1/4F+5)=0


Domain of the equation: 4F+5)!=0

F∈R


We get rid of parentheses

F-1/4F+8-5=0

We multiply all the terms by the denominator


F*4F+8*4F-5*4F-1=0

Wy multiply elements

4F^2+32F-20F-1=0

We add all the numbers together, and all the variables

4F^2+12F-1=0

a = 4; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*4}=\frac{-12-4\sqrt{10}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*4}=\frac{-12+4\sqrt{10}}{8}
$