3/7y-2/y=11

Solution for 3/7y-2/y=11 equation:

3/7y-2/y=11

We move all terms to the left:

3/7y-2/y-(11)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: y!=0

y∈R


We calculate fractions


3y/7y^2+(-14y)/7y^2-11=0

We multiply all the terms by the denominator


3y+(-14y)-11*7y^2=0

Wy multiply elements

-77y^2+3y+(-14y)=0

We get rid of parentheses

-77y^2+3y-14y=0

We add all the numbers together, and all the variables

-77y^2-11y=0

a = -77; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-77)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-77}=\frac{0}{-154}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-77}=\frac{22}{-154}
=-1/7
$