S+2/2x+1/x-3=3

Solution for S+2/2x+1/x-3=3 equation:

+2/2S+1/S-3=3

We move all terms to the left:

+2/2S+1/S-3-(3)=0


Domain of the equation: 2S!=0

S!=0/2

S!=0

S∈R



Domain of the equation: S!=0

S∈R


We add all the numbers together, and all the variables

2/2S+1/S-6=0

We calculate fractions


2S/2S^2+2S/2S^2-6=0

We multiply all the terms by the denominator


2S+2S-6*2S^2=0

We add all the numbers together, and all the variables

4S-6*2S^2=0

Wy multiply elements

-12S^2+4S=0

a = -12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-12}=\frac{-8}{-24}
=1/3
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-12}=\frac{0}{-24}
=0
$