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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


432x/648x^2+15x/648x^2+3x/648x^2-1=0

We multiply all the terms by the denominator


432x+15x+3x-1*648x^2=0

We add all the numbers together, and all the variables

450x-1*648x^2=0

Wy multiply elements

-648x^2+450x=0

a = -648; b = 450; c = 0;
Δ = b2-4ac
Δ = 4502-4·(-648)·0
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-450}{2*-648}=\frac{-900}{-1296}
=25/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+450}{2*-648}=\frac{0}{-1296}
=0
$