1/2y=y-60

Solution for 1/2y=y-60 equation:

1/2y=y-60

We move all terms to the left:

1/2y-(y-60)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+60=0

We multiply all the terms by the denominator


-y*2y+60*2y+1=0

Wy multiply elements

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

a = -2; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·(-2)·1
Δ = 14408
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:

$\sqrt{\Delta}=\sqrt{14408}=\sqrt{4*3602}=\sqrt{4}*\sqrt{3602}=2\sqrt{3602}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3602}}{2*-2}=\frac{-120-2\sqrt{3602}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3602}}{2*-2}=\frac{-120+2\sqrt{3602}}{-4}
$