1/7x-19/14=3/2x

Solution for 1/7x-19/14=3/2x equation:

1/7x-19/14=3/2x

We move all terms to the left:

1/7x-19/14-(3/2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x-(+3/2x)-19/14=0

We get rid of parentheses

1/7x-3/2x-19/14=0

We calculate fractions


(-532x^2)/196x^2+28x/196x^2+(-294x)/196x^2=0

We multiply all the terms by the denominator


(-532x^2)+28x+(-294x)=0

We get rid of parentheses

-532x^2+28x-294x=0

We add all the numbers together, and all the variables

-532x^2-266x=0

a = -532; b = -266; c = 0;
Δ = b2-4ac
Δ = -2662-4·(-532)·0
Δ = 70756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{70756}=266$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-266)-266}{2*-532}=\frac{0}{-1064}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-266)+266}{2*-532}=\frac{532}{-1064}
=-1/2
$