1/2x+1/x-x/2=0

Solution for 1/2x+1/x-x/2=0 equation:

1/2x+1/x-x/2=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


(-1x^2)/8x^2+x/8x^2+8x/8x^2=0

We multiply all the terms by the denominator


(-1x^2)+x+8x=0

We add all the numbers together, and all the variables

(-1x^2)+9x=0

We get rid of parentheses

-1x^2+9x=0

a = -1; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1}=\frac{0}{-2}
=0
$