5x-1/x+1=4

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

5x-1/x+1=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-1/x-3=0

We multiply all the terms by the denominator


5x*x-3*x-1=0

We add all the numbers together, and all the variables

-3x+5x*x-1=0

Wy multiply elements

5x^2-3x-1=0

a = 5; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·5·(-1)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{29}}{2*5}=\frac{3-\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{29}}{2*5}=\frac{3+\sqrt{29}}{10}
$