y=5/3y+2

Solution for y=5/3y+2 equation:

y=5/3y+2

We move all terms to the left:

y-(5/3y+2)=0


Domain of the equation: 3y+2)!=0

y∈R


We get rid of parentheses

y-5/3y-2=0

We multiply all the terms by the denominator


y*3y-2*3y-5=0

Wy multiply elements

3y^2-6y-5=0

a = 3; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·3·(-5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*3}=\frac{6-4\sqrt{6}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*3}=\frac{6+4\sqrt{6}}{6}
$