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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*3x-210*3x+4=0

Wy multiply elements

6x^2-630x+4=0

a = 6; b = -630; c = +4;
Δ = b2-4ac
Δ = -6302-4·6·4
Δ = 396804
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:

$\sqrt{\Delta}=\sqrt{396804}=\sqrt{4*99201}=\sqrt{4}*\sqrt{99201}=2\sqrt{99201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99201}}{2*6}=\frac{630-2\sqrt{99201}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99201}}{2*6}=\frac{630+2\sqrt{99201}}{12}
$