2s=1/2s+60

Solution for 2s=1/2s+60 equation:

2s=1/2s+60

We move all terms to the left:

2s-(1/2s+60)=0


Domain of the equation: 2s+60)!=0

s∈R


We get rid of parentheses

2s-1/2s-60=0

We multiply all the terms by the denominator


2s*2s-60*2s-1=0

Wy multiply elements

4s^2-120s-1=0

a = 4; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·4·(-1)
Δ = 14416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14416}=\sqrt{16*901}=\sqrt{16}*\sqrt{901}=4\sqrt{901}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{901}}{2*4}=\frac{120-4\sqrt{901}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{901}}{2*4}=\frac{120+4\sqrt{901}}{8}
$