3/7x-1+1/x=0

Solution for 3/7x-1+1/x=0 equation:

3/7x-1+1/x=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


3x/7x^2+7x/7x^2-1=0

We multiply all the terms by the denominator


3x+7x-1*7x^2=0

We add all the numbers together, and all the variables

10x-1*7x^2=0

Wy multiply elements

-7x^2+10x=0

a = -7; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-7)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-7}=\frac{-20}{-14}
=1+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-7}=\frac{0}{-14}
=0
$