y-2/3y=600

Solution for y-2/3y=600 equation:

y-2/3y=600

We move all terms to the left:

y-2/3y-(600)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply all the terms by the denominator


y*3y-600*3y-2=0

Wy multiply elements

3y^2-1800y-2=0

a = 3; b = -1800; c = -2;
Δ = b2-4ac
Δ = -18002-4·3·(-2)
Δ = 3240024
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:

$\sqrt{\Delta}=\sqrt{3240024}=\sqrt{4*810006}=\sqrt{4}*\sqrt{810006}=2\sqrt{810006}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1800)-2\sqrt{810006}}{2*3}=\frac{1800-2\sqrt{810006}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1800)+2\sqrt{810006}}{2*3}=\frac{1800+2\sqrt{810006}}{6}
$