y=1/3y+5

Solution for y=1/3y+5 equation:

y=1/3y+5

We move all terms to the left:

y-(1/3y+5)=0


Domain of the equation: 3y+5)!=0

y∈R


We get rid of parentheses

y-1/3y-5=0

We multiply all the terms by the denominator


y*3y-5*3y-1=0

Wy multiply elements

3y^2-15y-1=0

a = 3; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·3·(-1)
Δ = 237
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{237}}{2*3}=\frac{15-\sqrt{237}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{237}}{2*3}=\frac{15+\sqrt{237}}{6}
$