X-5/4x+1=X+7/x

Solution for X-5/4x+1=X+7/x equation:

X-5/4X+1=X+7/X

We move all terms to the left:

X-5/4X+1-(X+7/X)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R



Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-5/4X-(+X+7/X)+1=0

We get rid of parentheses

X-5/4X-X-7/X+1=0

We calculate fractions


X-X+(-5X)/4X^2+(-28X)/4X^2+1=0

We add all the numbers together, and all the variables

(-5X)/4X^2+(-28X)/4X^2+1=0

We multiply all the terms by the denominator


(-5X)+(-28X)+1*4X^2=0

Wy multiply elements

4X^2+(-5X)+(-28X)=0

We get rid of parentheses

4X^2-5X-28X=0

We add all the numbers together, and all the variables

4X^2-33X=0

a = 4; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·4·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*4}=\frac{66}{8}
=8+1/4
$