1/2y+60+y=180

Solution for 1/2y+60+y=180 equation:

1/2y+60+y=180

We move all terms to the left:

1/2y+60+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-120=0

We multiply all the terms by the denominator


y*2y-120*2y+1=0

Wy multiply elements

2y^2-240y+1=0

a = 2; b = -240; c = +1;
Δ = b2-4ac
Δ = -2402-4·2·1
Δ = 57592
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:

$\sqrt{\Delta}=\sqrt{57592}=\sqrt{4*14398}=\sqrt{4}*\sqrt{14398}=2\sqrt{14398}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14398}}{2*2}=\frac{240-2\sqrt{14398}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14398}}{2*2}=\frac{240+2\sqrt{14398}}{4}
$