4/7x-1/14=3/2x

Solution for 4/7x-1/14=3/2x equation:

4/7x-1/14=3/2x

We move all terms to the left:

4/7x-1/14-(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

4/7x-(+3/2x)-1/14=0

We get rid of parentheses

4/7x-3/2x-1/14=0

We calculate fractions


(-28x^2)/196x^2+112x/196x^2+(-294x)/196x^2=0

We multiply all the terms by the denominator


(-28x^2)+112x+(-294x)=0

We get rid of parentheses

-28x^2+112x-294x=0

We add all the numbers together, and all the variables

-28x^2-182x=0

a = -28; b = -182; c = 0;
Δ = b2-4ac
Δ = -1822-4·(-28)·0
Δ = 33124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33124}=182$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-182)-182}{2*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-182)+182}{2*-28}=\frac{364}{-56}
=-6+1/2
$