7/5y=y-0.32y

Solution for 7/5y=y-0.32y equation:

7/5y=y-0.32y

We move all terms to the left:

7/5y-(y-0.32y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

7/5y-(+0.68y)=0

We get rid of parentheses

7/5y-0.68y=0

We multiply all the terms by the denominator


-(0.68y)*5y+7=0

We add all the numbers together, and all the variables

-(+0.68y)*5y+7=0

We multiply parentheses

-0y^2+7=0

We add all the numbers together, and all the variables

-1y^2+7=0

a = -1; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-1)·7
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-1}=\frac{0-2\sqrt{7}}{-2}
=-\frac{2\sqrt{7}}{-2}
=-\frac{\sqrt{7}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-1}=\frac{0+2\sqrt{7}}{-2}
=\frac{2\sqrt{7}}{-2}
=\frac{\sqrt{7}}{-1}
$