F-1(X)=1/8x-1

Solution for F-1(X)=1/8x-1 equation:

-1(F)=1/8F-1

We move all terms to the left:

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


Domain of the equation: 8F-1)!=0

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8F^2+8F-1=0

a = -8; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-8)·(-1)
Δ = 32
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:

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