1/3s+s=12

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Solution for 1/3s+s=12 equation:



1/3s+s=12
We move all terms to the left:
1/3s+s-(12)=0
Domain of the equation: 3s!=0
s!=0/3
s!=0
s∈R
We add all the numbers together, and all the variables
s+1/3s-12=0
We multiply all the terms by the denominator
s*3s-12*3s+1=0
Wy multiply elements
3s^2-36s+1=0
a = 3; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·3·1
Δ = 1284
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:
$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{321}}{2*3}=\frac{36-2\sqrt{321}}{6} $
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{321}}{2*3}=\frac{36+2\sqrt{321}}{6} $

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