X-4+x+1+1/4x+5=9/4x+2

Solution for X-4+x+1+1/4x+5=9/4x+2 equation:

X-4+X+1+1/4X+5=9/4X+2

We move all terms to the left:

X-4+X+1+1/4X+5-(9/4X+2)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R



Domain of the equation: 4X+2)!=0

X∈R


We add all the numbers together, and all the variables

2X+1/4X-(9/4X+2)+2=0

We get rid of parentheses

2X+1/4X-9/4X-2+2=0

We multiply all the terms by the denominator


2X*4X-2*4X+2*4X+1-9=0

We add all the numbers together, and all the variables

2X*4X-2*4X+2*4X-8=0

Wy multiply elements

8X^2-8X+8X-8=0

We add all the numbers together, and all the variables

8X^2-8=0

a = 8; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·8·(-8)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*8}=\frac{-16}{16}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*8}=\frac{16}{16}
=1
$