1/2x-3+1/x-5=0

Solution for 1/2x-3+1/x-5=0 equation:

1/2x-3+1/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 add all the numbers together, and all the variables

1/2x+1/x-8=0

We calculate fractions


x/2x^2+2x/2x^2-8=0

We multiply all the terms by the denominator


x+2x-8*2x^2=0

We add all the numbers together, and all the variables

3x-8*2x^2=0

Wy multiply elements

-16x^2+3x=0

a = -16; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-16)·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*-16}=\frac{-6}{-32}
=3/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-16}=\frac{0}{-32}
=0
$