2y+1/2y+y=180

Solution for 2y+1/2y+y=180 equation:

2y+1/2y+y=180

We move all terms to the left:

2y+1/2y+y-(180)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3y+1/2y-180=0

We multiply all the terms by the denominator


3y*2y-180*2y+1=0

Wy multiply elements

6y^2-360y+1=0

a = 6; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·6·1
Δ = 129576
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:

$\sqrt{\Delta}=\sqrt{129576}=\sqrt{4*32394}=\sqrt{4}*\sqrt{32394}=2\sqrt{32394}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32394}}{2*6}=\frac{360-2\sqrt{32394}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32394}}{2*6}=\frac{360+2\sqrt{32394}}{12}
$