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

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

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

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y-1)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


2y/250y^2+875y/250y^2+(-6y)/250y^2+1=0

We multiply all the terms by the denominator


2y+875y+(-6y)+1*250y^2=0

We add all the numbers together, and all the variables

877y+(-6y)+1*250y^2=0

Wy multiply elements

250y^2+877y+(-6y)=0

We get rid of parentheses

250y^2+877y-6y=0

We add all the numbers together, and all the variables

250y^2+871y=0

a = 250; b = 871; c = 0;
Δ = b2-4ac
Δ = 8712-4·250·0
Δ = 758641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{758641}=871$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(871)-871}{2*250}=\frac{-1742}{500}
=-3+121/250
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(871)+871}{2*250}=\frac{0}{500}
=0
$