(y/5)-(y-30/8=2y

Solution for (y/5)-(y-30/8=2y equation:

(y/5)-(y-30/8=2y

We move all terms to the left:

(y/5)-(y-30/8-(2y)=0


Domain of the equation: 8-2y!=0

We move all terms containing y to the left, all other terms to the right

-2y!=-8

y!=-8/-2

y!=+4

y∈R


We add all the numbers together, and all the variables

(+y/5)-(y-30/8-2y=0

We get rid of parentheses

y/5-(y-30/8-2y=0

We calculate fractions


6y/(-2y+40)+(-(y-30*5)/(-2y+40)=0


We calculate terms in parentheses: +(-(y-30*5)/(-2y+40), so:

-(y-30*5)/(-2y+40

We add all the numbers together, and all the variables

-(y-150)/(-2y+40

We multiply all the terms by the denominator


-(y-150)

We get rid of parentheses

-y+150

We add all the numbers together, and all the variables

-1y+150

Back to the equation:

+(-1y+150)


We get rid of parentheses

6y/(-2y+40)-1y+150=0

We multiply all the terms by the denominator


6y-1y*(-2y+40)+150*(-2y+40)=0

We multiply parentheses

2y^2+6y-40y-300y+6000=0

We add all the numbers together, and all the variables

2y^2-334y+6000=0

a = 2; b = -334; c = +6000;
Δ = b2-4ac
Δ = -3342-4·2·6000
Δ = 63556
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:

$\sqrt{\Delta}=\sqrt{63556}=\sqrt{4*15889}=\sqrt{4}*\sqrt{15889}=2\sqrt{15889}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-334)-2\sqrt{15889}}{2*2}=\frac{334-2\sqrt{15889}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-334)+2\sqrt{15889}}{2*2}=\frac{334+2\sqrt{15889}}{4}
$