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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


144x^2/108x^2+54x/108x^2+90x/108x^2+2=0

We multiply all the terms by the denominator


144x^2+54x+90x+2*108x^2=0

We add all the numbers together, and all the variables

144x^2+144x+2*108x^2=0

Wy multiply elements

144x^2+216x^2+144x=0

We add all the numbers together, and all the variables

360x^2+144x=0

a = 360; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·360·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*360}=\frac{-288}{720}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*360}=\frac{0}{720}
=0
$