2/3x-1/8=2-5/6x

Solution for 2/3x-1/8=2-5/6x equation:

2/3x-1/8=2-5/6x

We move all terms to the left:

2/3x-1/8-(2-5/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-5/6x+2)-1/8=0

We get rid of parentheses

2/3x+5/6x-2-1/8=0

We calculate fractions


(-108x^2)/1152x^2+768x/1152x^2+960x/1152x^2-2=0

We multiply all the terms by the denominator


(-108x^2)+768x+960x-2*1152x^2=0

We add all the numbers together, and all the variables

(-108x^2)+1728x-2*1152x^2=0

Wy multiply elements

(-108x^2)-2304x^2+1728x=0

We get rid of parentheses

-108x^2-2304x^2+1728x=0

We add all the numbers together, and all the variables

-2412x^2+1728x=0

a = -2412; b = 1728; c = 0;
Δ = b2-4ac
Δ = 17282-4·(-2412)·0
Δ = 2985984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2985984}=1728$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1728)-1728}{2*-2412}=\frac{-3456}{-4824}
=48/67
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1728)+1728}{2*-2412}=\frac{0}{-4824}
=0
$