5-2/3y=y+15

Solution for 5-2/3y=y+15 equation:

5-2/3y=y+15

We move all terms to the left:

5-2/3y-(y+15)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

-2/3y-y-15+5=0

We multiply all the terms by the denominator


-y*3y-15*3y+5*3y-2=0

Wy multiply elements

-3y^2-45y+15y-2=0

We add all the numbers together, and all the variables

-3y^2-30y-2=0

a = -3; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·(-3)·(-2)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*-3}=\frac{30-2\sqrt{219}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*-3}=\frac{30+2\sqrt{219}}{-6}
$