1/6x-2/3x=650

Solution for 1/6x-2/3x=650 equation:

1/6x-2/3x=650

We move all terms to the left:

1/6x-2/3x-(650)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


3x/18x^2+(-12x)/18x^2-650=0

We multiply all the terms by the denominator


3x+(-12x)-650*18x^2=0

Wy multiply elements

-11700x^2+3x+(-12x)=0

We get rid of parentheses

-11700x^2+3x-12x=0

We add all the numbers together, and all the variables

-11700x^2-9x=0

a = -11700; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-11700)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-11700}=\frac{0}{-23400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-11700}=\frac{18}{-23400}
=-1/1300
$