1/2x+1/x=30

Solution for 1/2x+1/x=30 equation:

1/2x+1/x=30

We move all terms to the left:

1/2x+1/x-(30)=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+2x/2x^2-30=0

We multiply all the terms by the denominator


x+2x-30*2x^2=0

We add all the numbers together, and all the variables

3x-30*2x^2=0

Wy multiply elements

-60x^2+3x=0

a = -60; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-60)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-60}=\frac{-6}{-120}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-60}=\frac{0}{-120}
=0
$