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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/18x^2+15x/18x^2-3=0

We multiply all the terms by the denominator


12x+15x-3*18x^2=0

We add all the numbers together, and all the variables

27x-3*18x^2=0

Wy multiply elements

-54x^2+27x=0

a = -54; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-54)·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*-54}=\frac{-54}{-108}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-54}=\frac{0}{-108}
=0
$