6y/y+6=y-1

Solution for 6y/y+6=y-1 equation:

6y/y+6=y-1

We move all terms to the left:

6y/y+6-(y-1)=0


Domain of the equation: y!=0

y∈R


We get rid of parentheses

6y/y-y+1+6=0

We multiply all the terms by the denominator


6y-y*y+1*y+6*y=0

We add all the numbers together, and all the variables

13y-y*y=0

Wy multiply elements

-1y^2+13y=0

a = -1; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1}=\frac{-26}{-2}
=+13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1}=\frac{0}{-2}
=0
$