5x-11=4/x

Solution for 5x-11=4/x equation:

5x-11=4/x

We move all terms to the left:

5x-11-(4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+4/x)-11=0

We get rid of parentheses

5x-4/x-11=0

We multiply all the terms by the denominator


5x*x-11*x-4=0

We add all the numbers together, and all the variables

-11x+5x*x-4=0

Wy multiply elements

5x^2-11x-4=0

a = 5; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·5·(-4)
Δ = 201
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{-(-11)-\sqrt{201}}{2*5}=\frac{11-\sqrt{201}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{201}}{2*5}=\frac{11+\sqrt{201}}{10}
$