(y-62)=2/3y

Solution for (y-62)=2/3y equation:

(y-62)=2/3y

We move all terms to the left:

(y-62)-(2/3y)=0


Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(y-62)-(+2/3y)=0

We get rid of parentheses

y-2/3y-62=0

We multiply all the terms by the denominator


y*3y-62*3y-2=0

Wy multiply elements

3y^2-186y-2=0

a = 3; b = -186; c = -2;
Δ = b2-4ac
Δ = -1862-4·3·(-2)
Δ = 34620
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:

$\sqrt{\Delta}=\sqrt{34620}=\sqrt{4*8655}=\sqrt{4}*\sqrt{8655}=2\sqrt{8655}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-2\sqrt{8655}}{2*3}=\frac{186-2\sqrt{8655}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+2\sqrt{8655}}{2*3}=\frac{186+2\sqrt{8655}}{6}
$