2/3y=y-20

Solution for 2/3y=y-20 equation:

2/3y=y-20

We move all terms to the left:

2/3y-(y-20)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

2/3y-y+20=0

We multiply all the terms by the denominator


-y*3y+20*3y+2=0

Wy multiply elements

-3y^2+60y+2=0

a = -3; b = 60; c = +2;
Δ = b2-4ac
Δ = 602-4·(-3)·2
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{906}}{2*-3}=\frac{-60-2\sqrt{906}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{906}}{2*-3}=\frac{-60+2\sqrt{906}}{-6}
$