X+2/3x+x+2/3x=310

Solution for X+2/3x+x+2/3x=310 equation:

X+2/3X+X+2/3X=310

We move all terms to the left:

X+2/3X+X+2/3X-(310)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

2X+2/3X+2/3X-310=0

We multiply all the terms by the denominator


2X*3X-310*3X+2+2=0

We add all the numbers together, and all the variables

2X*3X-310*3X+4=0

Wy multiply elements

6X^2-930X+4=0

a = 6; b = -930; c = +4;
Δ = b2-4ac
Δ = -9302-4·6·4
Δ = 864804
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:

$\sqrt{\Delta}=\sqrt{864804}=\sqrt{4*216201}=\sqrt{4}*\sqrt{216201}=2\sqrt{216201}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-930)-2\sqrt{216201}}{2*6}=\frac{930-2\sqrt{216201}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-930)+2\sqrt{216201}}{2*6}=\frac{930+2\sqrt{216201}}{12}
$