s+21/2s+10s=31

Solution for s+21/2s+10s=31 equation:

s+21/2s+10s=31

We move all terms to the left:

s+21/2s+10s-(31)=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+21/2s-31=0

We multiply all the terms by the denominator


11s*2s-31*2s+21=0

Wy multiply elements

22s^2-62s+21=0

a = 22; b = -62; c = +21;
Δ = b2-4ac
Δ = -622-4·22·21
Δ = 1996
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:

$\sqrt{\Delta}=\sqrt{1996}=\sqrt{4*499}=\sqrt{4}*\sqrt{499}=2\sqrt{499}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-2\sqrt{499}}{2*22}=\frac{62-2\sqrt{499}}{44}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+2\sqrt{499}}{2*22}=\frac{62+2\sqrt{499}}{44}
$