1/7y+5=1/5y

Solution for 1/7y+5=1/5y equation:

1/7y+5=1/5y

We move all terms to the left:

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


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/7y-1/5y+5=0

We calculate fractions


5y/35y^2+(-7y)/35y^2+5=0

We multiply all the terms by the denominator


5y+(-7y)+5*35y^2=0

Wy multiply elements

175y^2+5y+(-7y)=0

We get rid of parentheses

175y^2+5y-7y=0

We add all the numbers together, and all the variables

175y^2-2y=0

a = 175; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·175·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*175}=\frac{0}{350}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*175}=\frac{4}{350}
=2/175
$