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

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

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

We move all terms to the left:

2/3x-3/2x-(-5/6)=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 get rid of parentheses

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

We calculate fractions


60x^2/216x^2+144x/216x^2+(-324x)/216x^2=0

We multiply all the terms by the denominator


60x^2+144x+(-324x)=0

We get rid of parentheses

60x^2+144x-324x=0

We add all the numbers together, and all the variables

60x^2-180x=0

a = 60; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·60·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*60}=\frac{360}{120}
=3
$