s+1/2s+10s=64

Solution for s+1/2s+10s=64 equation:

s+1/2s+10s=64

We move all terms to the left:

s+1/2s+10s-(64)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

11s+1/2s-64=0

We multiply all the terms by the denominator


11s*2s-64*2s+1=0

Wy multiply elements

22s^2-128s+1=0

a = 22; b = -128; c = +1;
Δ = b2-4ac
Δ = -1282-4·22·1
Δ = 16296
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:

$\sqrt{\Delta}=\sqrt{16296}=\sqrt{4*4074}=\sqrt{4}*\sqrt{4074}=2\sqrt{4074}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-2\sqrt{4074}}{2*22}=\frac{128-2\sqrt{4074}}{44}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+2\sqrt{4074}}{2*22}=\frac{128+2\sqrt{4074}}{44}
$