3/7y+1/7=1/8y+2

Solution for 3/7y+1/7=1/8y+2 equation:

3/7y+1/7=1/8y+2

We move all terms to the left:

3/7y+1/7-(1/8y+2)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 8y+2)!=0

y∈R


We get rid of parentheses

3/7y-1/8y-2+1/7=0

We calculate fractions


24y/2744y^2+(-343y)/2744y^2+8y/2744y^2-2=0

We multiply all the terms by the denominator


24y+(-343y)+8y-2*2744y^2=0

We add all the numbers together, and all the variables

32y+(-343y)-2*2744y^2=0

Wy multiply elements

-5488y^2+32y+(-343y)=0

We get rid of parentheses

-5488y^2+32y-343y=0

We add all the numbers together, and all the variables

-5488y^2-311y=0

a = -5488; b = -311; c = 0;
Δ = b2-4ac
Δ = -3112-4·(-5488)·0
Δ = 96721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{96721}=311$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-311)-311}{2*-5488}=\frac{0}{-10976}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-311)+311}{2*-5488}=\frac{622}{-10976}
=-311/5488
$