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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


12x^2/216x^2+144x/216x^2+(-108x)/216x^2-2=0

We multiply all the terms by the denominator


12x^2+144x+(-108x)-2*216x^2=0

Wy multiply elements

12x^2-432x^2+144x+(-108x)=0

We get rid of parentheses

12x^2-432x^2+144x-108x=0

We add all the numbers together, and all the variables

-420x^2+36x=0

a = -420; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-420)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-420}=\frac{-72}{-840}
=3/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-420}=\frac{0}{-840}
=0
$