4/3y+y+8/3y=180

Solution for 4/3y+y+8/3y=180 equation:

4/3y+y+8/3y=180

We move all terms to the left:

4/3y+y+8/3y-(180)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+4/3y+8/3y-180=0

We multiply all the terms by the denominator


y*3y-180*3y+4+8=0

We add all the numbers together, and all the variables

y*3y-180*3y+12=0

Wy multiply elements

3y^2-540y+12=0

a = 3; b = -540; c = +12;
Δ = b2-4ac
Δ = -5402-4·3·12
Δ = 291456
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:

$\sqrt{\Delta}=\sqrt{291456}=\sqrt{576*506}=\sqrt{576}*\sqrt{506}=24\sqrt{506}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-24\sqrt{506}}{2*3}=\frac{540-24\sqrt{506}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+24\sqrt{506}}{2*3}=\frac{540+24\sqrt{506}}{6}
$