x+1/3X=3200

Solution for x+1/3X=3200 equation:

x+1/3x=3200

We move all terms to the left:

x+1/3x-(3200)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-3200*3x+1=0

Wy multiply elements

3x^2-9600x+1=0

a = 3; b = -9600; c = +1;
Δ = b2-4ac
Δ = -96002-4·3·1
Δ = 92159988
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:

$\sqrt{\Delta}=\sqrt{92159988}=\sqrt{4*23039997}=\sqrt{4}*\sqrt{23039997}=2\sqrt{23039997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9600)-2\sqrt{23039997}}{2*3}=\frac{9600-2\sqrt{23039997}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9600)+2\sqrt{23039997}}{2*3}=\frac{9600+2\sqrt{23039997}}{6}
$