3x+48=1/3x

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Solution for 3x+48=1/3x equation:



3x+48=1/3x
We move all terms to the left:
3x+48-(1/3x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3x-(+1/3x)+48=0
We get rid of parentheses
3x-1/3x+48=0
We multiply all the terms by the denominator
3x*3x+48*3x-1=0
Wy multiply elements
9x^2+144x-1=0
a = 9; b = 144; c = -1;
Δ = b2-4ac
Δ = 1442-4·9·(-1)
Δ = 20772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{20772}=\sqrt{36*577}=\sqrt{36}*\sqrt{577}=6\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-6\sqrt{577}}{2*9}=\frac{-144-6\sqrt{577}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+6\sqrt{577}}{2*9}=\frac{-144+6\sqrt{577}}{18} $

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