X+4+1/3x=20

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Solution for X+4+1/3x=20 equation:



X+4+1/3X=20
We move all terms to the left:
X+4+1/3X-(20)=0
Domain of the equation: 3X!=0
X!=0/3
X!=0
X∈R
We add all the numbers together, and all the variables
X+1/3X-16=0
We multiply all the terms by the denominator
X*3X-16*3X+1=0
Wy multiply elements
3X^2-48X+1=0
a = 3; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·3·1
Δ = 2292
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:
$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{573}}{2*3}=\frac{48-2\sqrt{573}}{6} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{573}}{2*3}=\frac{48+2\sqrt{573}}{6} $

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