1/2y+27+y=180

Solution for 1/2y+27+y=180 equation:

1/2y+27+y=180

We move all terms to the left:

1/2y+27+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

y+1/2y-153=0

We multiply all the terms by the denominator


y*2y-153*2y+1=0

Wy multiply elements

2y^2-306y+1=0

a = 2; b = -306; c = +1;
Δ = b2-4ac
Δ = -3062-4·2·1
Δ = 93628
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:

$\sqrt{\Delta}=\sqrt{93628}=\sqrt{4*23407}=\sqrt{4}*\sqrt{23407}=2\sqrt{23407}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-306)-2\sqrt{23407}}{2*2}=\frac{306-2\sqrt{23407}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-306)+2\sqrt{23407}}{2*2}=\frac{306+2\sqrt{23407}}{4}
$