2/3y+y=180

Solution for 2/3y+y=180 equation:

2/3y+y=180

We move all terms to the left:

2/3y+y-(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+2/3y-180=0

We multiply all the terms by the denominator


y*3y-180*3y+2=0

Wy multiply elements

3y^2-540y+2=0

a = 3; b = -540; c = +2;
Δ = b2-4ac
Δ = -5402-4·3·2
Δ = 291576
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:

$\sqrt{\Delta}=\sqrt{291576}=\sqrt{4*72894}=\sqrt{4}*\sqrt{72894}=2\sqrt{72894}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72894}}{2*3}=\frac{540-2\sqrt{72894}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72894}}{2*3}=\frac{540+2\sqrt{72894}}{6}
$