2/7y-3=1/2y

Solution for 2/7y-3=1/2y equation:

2/7y-3=1/2y

We move all terms to the left:

2/7y-3-(1/2y)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2/7y-(+1/2y)-3=0

We get rid of parentheses

2/7y-1/2y-3=0

We calculate fractions


4y/14y^2+(-7y)/14y^2-3=0

We multiply all the terms by the denominator


4y+(-7y)-3*14y^2=0

Wy multiply elements

-42y^2+4y+(-7y)=0

We get rid of parentheses

-42y^2+4y-7y=0

We add all the numbers together, and all the variables

-42y^2-3y=0

a = -42; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-42)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-42}=\frac{0}{-84}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-42}=\frac{6}{-84}
=-1/14
$