5/x+x-4/2=11

Solution for 5/x+x-4/2=11 equation:

5/x+x-4/2=11

We move all terms to the left:

5/x+x-4/2-(11)=0


Domain of the equation: x!=0

x∈R


determiningTheFunctionDomain
5/x+x-11-4/2=0

We add all the numbers together, and all the variables

x+5/x-13=0

We multiply all the terms by the denominator


x*x-13*x+5=0

We add all the numbers together, and all the variables

-13x+x*x+5=0

Wy multiply elements

x^2-13x+5=0

a = 1; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·1·5
Δ = 149
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{-(-13)-\sqrt{149}}{2*1}=\frac{13-\sqrt{149}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{149}}{2*1}=\frac{13+\sqrt{149}}{2}
$