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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


15x/18x^2+12x/18x^2-1=0

We multiply all the terms by the denominator


15x+12x-1*18x^2=0

We add all the numbers together, and all the variables

27x-1*18x^2=0

Wy multiply elements

-18x^2+27x=0

a = -18; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-18)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-18}=\frac{-54}{-36}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-18}=\frac{0}{-36}
=0
$