5/3y=y-8

Solution for 5/3y=y-8 equation:

5/3y=y-8

We move all terms to the left:

5/3y-(y-8)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

5/3y-y+8=0

We multiply all the terms by the denominator


-y*3y+8*3y+5=0

Wy multiply elements

-3y^2+24y+5=0

a = -3; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·(-3)·5
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{159}}{2*-3}=\frac{-24-2\sqrt{159}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{159}}{2*-3}=\frac{-24+2\sqrt{159}}{-6}
$