x+1=2+x/4x

Solution for x+1=2+x/4x equation:

x+1=2+x/4x

We move all terms to the left:

x+1-(2+x/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(x/4x+2)+1=0

We get rid of parentheses

x-x/4x-2+1=0

We multiply all the terms by the denominator


x*4x-x-2*4x+1*4x=0

We add all the numbers together, and all the variables

-1x+x*4x-2*4x+1*4x=0

Wy multiply elements

4x^2-1x-8x+4x=0

We add all the numbers together, and all the variables

4x^2-5x=0

a = 4; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·4·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*4}=\frac{10}{8}
=1+1/4
$