2+21/2s+20s=41

Solution for 2+21/2s+20s=41 equation:

2+21/2s+20s=41

We move all terms to the left:

2+21/2s+20s-(41)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

20s+21/2s-39=0

We multiply all the terms by the denominator


20s*2s-39*2s+21=0

Wy multiply elements

40s^2-78s+21=0

a = 40; b = -78; c = +21;
Δ = b2-4ac
Δ = -782-4·40·21
Δ = 2724
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:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{681}}{2*40}=\frac{78-2\sqrt{681}}{80}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{681}}{2*40}=\frac{78+2\sqrt{681}}{80}
$