13=1/6y+2y

Solution for 13=1/6y+2y equation:

13=1/6y+2y

We move all terms to the left:

13-(1/6y+2y)=0


Domain of the equation: 6y+2y)!=0

y∈R


We add all the numbers together, and all the variables

-(+2y+1/6y)+13=0

We get rid of parentheses

-2y-1/6y+13=0

We multiply all the terms by the denominator


-2y*6y+13*6y-1=0

Wy multiply elements

-12y^2+78y-1=0

a = -12; b = 78; c = -1;
Δ = b2-4ac
Δ = 782-4·(-12)·(-1)
Δ = 6036
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:

$\sqrt{\Delta}=\sqrt{6036}=\sqrt{4*1509}=\sqrt{4}*\sqrt{1509}=2\sqrt{1509}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1509}}{2*-12}=\frac{-78-2\sqrt{1509}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1509}}{2*-12}=\frac{-78+2\sqrt{1509}}{-24}
$