S+31/2s+10s=46

Solution for S+31/2s+10s=46 equation:

+31/2S+10S=46

We move all terms to the left:

+31/2S+10S-(46)=0


Domain of the equation: 2S!=0

S!=0/2

S!=0

S∈R


We add all the numbers together, and all the variables

10S+31/2S-46=0

We multiply all the terms by the denominator


10S*2S-46*2S+31=0

Wy multiply elements

20S^2-92S+31=0

a = 20; b = -92; c = +31;
Δ = b2-4ac
Δ = -922-4·20·31
Δ = 5984
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:

$\sqrt{\Delta}=\sqrt{5984}=\sqrt{16*374}=\sqrt{16}*\sqrt{374}=4\sqrt{374}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{374}}{2*20}=\frac{92-4\sqrt{374}}{40}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{374}}{2*20}=\frac{92+4\sqrt{374}}{40}
$