-1/6*y+y=1

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

-1/6y+y=1

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

y-1/6y-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

6y^2-6y-1=0

a = 6; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·6·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*6}=\frac{6-2\sqrt{15}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*6}=\frac{6+2\sqrt{15}}{12}
$