2/x-2-3/7x-14=-2

Solution for 2/x-2-3/7x-14=-2 equation:

2/x-2-3/7x-14=-2

We move all terms to the left:

2/x-2-3/7x-14-(-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-3/7x-14=0

We calculate fractions


14x/7x^2+(-3x)/7x^2-14=0

We multiply all the terms by the denominator


14x+(-3x)-14*7x^2=0

Wy multiply elements

-98x^2+14x+(-3x)=0

We get rid of parentheses

-98x^2+14x-3x=0

We add all the numbers together, and all the variables

-98x^2+11x=0

a = -98; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-98)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-98}=\frac{-22}{-196}
=11/98
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-98}=\frac{0}{-196}
=0
$