1/2y-5=1/7y

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

1/2y-5=1/7y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


7y/14y^2+(-2y)/14y^2-5=0

We multiply all the terms by the denominator


7y+(-2y)-5*14y^2=0

Wy multiply elements

-70y^2+7y+(-2y)=0

We get rid of parentheses

-70y^2+7y-2y=0

We add all the numbers together, and all the variables

-70y^2+5y=0

a = -70; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-70)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-70}=\frac{-10}{-140}
=1/14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-70}=\frac{0}{-140}
=0
$