1/2x+13/x=5

Solution for 1/2x+13/x=5 equation:

1/2x+13/x=5

We move all terms to the left:

1/2x+13/x-(5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


x/2x^2+26x/2x^2-5=0

We multiply all the terms by the denominator


x+26x-5*2x^2=0

We add all the numbers together, and all the variables

27x-5*2x^2=0

Wy multiply elements

-10x^2+27x=0

a = -10; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-10)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-10}=\frac{-54}{-20}
=2+7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-10}=\frac{0}{-20}
=0
$