2/7x-5/2=-3/14x+1

Solution for 2/7x-5/2=-3/14x+1 equation:

2/7x-5/2=-3/14x+1

We move all terms to the left:

2/7x-5/2-(-3/14x+1)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x+1)!=0

x∈R


We get rid of parentheses

2/7x+3/14x-1-5/2=0

We calculate fractions


(-490x^2)/392x^2+112x/392x^2+84x/392x^2-1=0

We multiply all the terms by the denominator


(-490x^2)+112x+84x-1*392x^2=0

We add all the numbers together, and all the variables

(-490x^2)+196x-1*392x^2=0

Wy multiply elements

(-490x^2)-392x^2+196x=0

We get rid of parentheses

-490x^2-392x^2+196x=0

We add all the numbers together, and all the variables

-882x^2+196x=0

a = -882; b = 196; c = 0;
Δ = b2-4ac
Δ = 1962-4·(-882)·0
Δ = 38416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38416}=196$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-196}{2*-882}=\frac{-392}{-1764}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+196}{2*-882}=\frac{0}{-1764}
=0
$