7/5y=y-2/5y

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

7/5y=y-2/5y

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-y*5y+7+2=0

We add all the numbers together, and all the variables

-y*5y+9=0

Wy multiply elements

-5y^2+9=0

a = -5; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-5)·9
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-5}=\frac{0-6\sqrt{5}}{-10}
=-\frac{6\sqrt{5}}{-10}
=-\frac{3\sqrt{5}}{-5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-5}=\frac{0+6\sqrt{5}}{-10}
=\frac{6\sqrt{5}}{-10}
=\frac{3\sqrt{5}}{-5}
$