x-(1/3x)=1730

Solution for x-(1/3x)=1730 equation:

x-(1/3x)=1730

We move all terms to the left:

x-(1/3x)-(1730)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/3x)-1730=0

We get rid of parentheses

x-1/3x-1730=0

We multiply all the terms by the denominator


x*3x-1730*3x-1=0

Wy multiply elements

3x^2-5190x-1=0

a = 3; b = -5190; c = -1;
Δ = b2-4ac
Δ = -51902-4·3·(-1)
Δ = 26936112
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:

$\sqrt{\Delta}=\sqrt{26936112}=\sqrt{16*1683507}=\sqrt{16}*\sqrt{1683507}=4\sqrt{1683507}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5190)-4\sqrt{1683507}}{2*3}=\frac{5190-4\sqrt{1683507}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5190)+4\sqrt{1683507}}{2*3}=\frac{5190+4\sqrt{1683507}}{6}
$