3y=13+1/6y

Solution for 3y=13+1/6y equation:

3y=13+1/6y

We move all terms to the left:

3y-(13+1/6y)=0


Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3y-(1/6y+13)=0

We get rid of parentheses

3y-1/6y-13=0

We multiply all the terms by the denominator


3y*6y-13*6y-1=0

Wy multiply elements

18y^2-78y-1=0

a = 18; b = -78; c = -1;
Δ = b2-4ac
Δ = -782-4·18·(-1)
Δ = 6156
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:

$\sqrt{\Delta}=\sqrt{6156}=\sqrt{324*19}=\sqrt{324}*\sqrt{19}=18\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-18\sqrt{19}}{2*18}=\frac{78-18\sqrt{19}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+18\sqrt{19}}{2*18}=\frac{78+18\sqrt{19}}{36}
$