x=1/4x+1

Solution for x=1/4x+1 equation:

x=1/4x+1

We move all terms to the left:

x-(1/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

x-1/4x-1=0

We multiply all the terms by the denominator


x*4x-1*4x-1=0

Wy multiply elements

4x^2-4x-1=0

a = 4; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·4·(-1)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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