2/3x-7/6=2-1/2x

Solution for 2/3x-7/6=2-1/2x equation:

2/3x-7/6=2-1/2x

We move all terms to the left:

2/3x-7/6-(2-1/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1/2x+2)-7/6=0

We get rid of parentheses

2/3x+1/2x-2-7/6=0

We calculate fractions


(-84x^2)/216x^2+144x/216x^2+108x/216x^2-2=0

We multiply all the terms by the denominator


(-84x^2)+144x+108x-2*216x^2=0

We add all the numbers together, and all the variables

(-84x^2)+252x-2*216x^2=0

Wy multiply elements

(-84x^2)-432x^2+252x=0

We get rid of parentheses

-84x^2-432x^2+252x=0

We add all the numbers together, and all the variables

-516x^2+252x=0

a = -516; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-516)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-516}=\frac{-504}{-1032}
=21/43
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-516}=\frac{0}{-1032}
=0
$