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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


84x^2/216x^2+144x/216x^2+324x/216x^2-1=0

We multiply all the terms by the denominator


84x^2+144x+324x-1*216x^2=0

We add all the numbers together, and all the variables

84x^2+468x-1*216x^2=0

Wy multiply elements

84x^2-216x^2+468x=0

We add all the numbers together, and all the variables

-132x^2+468x=0

a = -132; b = 468; c = 0;
Δ = b2-4ac
Δ = 4682-4·(-132)·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(468)-468}{2*-132}=\frac{-936}{-264}
=3+6/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(468)+468}{2*-132}=\frac{0}{-264}
=0
$