5/4x+(x+1)/x=2

Solution for 5/4x+(x+1)/x=2 equation:

5/4x+(x+1)/x=2

We move all terms to the left:

5/4x+(x+1)/x-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


5x/4x^2+(4x^2+4x)/4x^2-2=0

We multiply all the terms by the denominator


5x+(4x^2+4x)-2*4x^2=0

Wy multiply elements

-8x^2+5x+(4x^2+4x)=0

We get rid of parentheses

-8x^2+4x^2+5x+4x=0

We add all the numbers together, and all the variables

-4x^2+9x=0

a = -4; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-4)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-4}=\frac{0}{-8}
=0
$