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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x*7x-2*7x+5=0

Wy multiply elements

-21x^2-14x+5=0

a = -21; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·(-21)·5
Δ = 616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{154}}{2*-21}=\frac{14-2\sqrt{154}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{154}}{2*-21}=\frac{14+2\sqrt{154}}{-42}
$