2/3(y)=y-62

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

2/3(y)=y-62

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

2/3y-y+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}
$