x+2/3x=210

Solution for x+2/3x=210 equation:

x+2/3x=210

We move all terms to the left:

x+2/3x-(210)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-210*3x+2=0

Wy multiply elements

3x^2-630x+2=0

a = 3; b = -630; c = +2;
Δ = b2-4ac
Δ = -6302-4·3·2
Δ = 396876
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:

$\sqrt{\Delta}=\sqrt{396876}=\sqrt{4*99219}=\sqrt{4}*\sqrt{99219}=2\sqrt{99219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99219}}{2*3}=\frac{630-2\sqrt{99219}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99219}}{2*3}=\frac{630+2\sqrt{99219}}{6}
$