(5/3y)-(2/7y)=1

Solution for (5/3y)-(2/7y)=1 equation:

(5/3y)-(2/7y)=1

We move all terms to the left:

(5/3y)-(2/7y)-(1)=0


Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R



Domain of the equation: 7y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+5/3y)-(+2/7y)-1=0

We get rid of parentheses

5/3y-2/7y-1=0

We calculate fractions


35y/21y^2+(-6y)/21y^2-1=0

We multiply all the terms by the denominator


35y+(-6y)-1*21y^2=0

Wy multiply elements

-21y^2+35y+(-6y)=0

We get rid of parentheses

-21y^2+35y-6y=0

We add all the numbers together, and all the variables

-21y^2+29y=0

a = -21; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-21)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-21}=\frac{-58}{-42}
=1+8/21
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-21}=\frac{0}{-42}
=0
$