1x+2/3x=230

Solution for 1x+2/3x=230 equation:

1x+2/3x=230

We move all terms to the left:

1x+2/3x-(230)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/3x-230=0

We multiply all the terms by the denominator


x*3x-230*3x+2=0

Wy multiply elements

3x^2-690x+2=0

a = 3; b = -690; c = +2;
Δ = b2-4ac
Δ = -6902-4·3·2
Δ = 476076
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:

$\sqrt{\Delta}=\sqrt{476076}=\sqrt{4*119019}=\sqrt{4}*\sqrt{119019}=2\sqrt{119019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-690)-2\sqrt{119019}}{2*3}=\frac{690-2\sqrt{119019}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-690)+2\sqrt{119019}}{2*3}=\frac{690+2\sqrt{119019}}{6}
$