(1/x)+(1/2x)=7

Solution for (1/x)+(1/2x)=7 equation:

(1/x)+(1/2x)=7

We move all terms to the left:

(1/x)+(1/2x)-(7)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/x)+(+1/2x)-7=0

We get rid of parentheses

1/x+1/2x-7=0

We calculate fractions


2x/2x^2+x/2x^2-7=0

We multiply all the terms by the denominator


2x+x-7*2x^2=0

We add all the numbers together, and all the variables

3x-7*2x^2=0

Wy multiply elements

-14x^2+3x=0

a = -14; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-14)·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*-14}=\frac{-6}{-28}
=3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-14}=\frac{0}{-28}
=0
$