10/7x-2/x=2

Solution for 10/7x-2/x=2 equation:

10/7x-2/x=2

We move all terms to the left:

10/7x-2/x-(2)=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


10x/7x^2+(-14x)/7x^2-2=0

We multiply all the terms by the denominator


10x+(-14x)-2*7x^2=0

Wy multiply elements

-14x^2+10x+(-14x)=0

We get rid of parentheses

-14x^2+10x-14x=0

We add all the numbers together, and all the variables

-14x^2-4x=0

a = -14; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-14)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-14}=\frac{8}{-28}
=-2/7
$