6/y+4+1=5/2y+8

Solution for 6/y+4+1=5/2y+8 equation:

6/y+4+1=5/2y+8

We move all terms to the left:

6/y+4+1-(5/2y+8)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y+8)!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6/y-5/2y-8+5=0

We calculate fractions


12y/2y^2+(-5y)/2y^2-8+5=0

We add all the numbers together, and all the variables

12y/2y^2+(-5y)/2y^2-3=0

We multiply all the terms by the denominator


12y+(-5y)-3*2y^2=0

Wy multiply elements

-6y^2+12y+(-5y)=0

We get rid of parentheses

-6y^2+12y-5y=0

We add all the numbers together, and all the variables

-6y^2+7y=0

a = -6; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-6)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-6}=\frac{-14}{-12}
=1+1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-6}=\frac{0}{-12}
=0
$