5/4x+x+1=9/4x+1

Solution for 5/4x+x+1=9/4x+1 equation:

5/4x+x+1=9/4x+1

We move all terms to the left:

5/4x+x+1-(9/4x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

x+5/4x-(9/4x+1)+1=0

We get rid of parentheses

x+5/4x-9/4x-1+1=0

We multiply all the terms by the denominator


x*4x-1*4x+1*4x+5-9=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-4=0

a = 4; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·4·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*4}=\frac{8}{8}
=1
$