-8/3x+3/2x=-7/6

Solution for -8/3x+3/2x=-7/6 equation:

-8/3x+3/2x=-7/6

We move all terms to the left:

-8/3x+3/2x-(-7/6)=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

-8/3x+3/2x+7/6=0

We calculate fractions


84x^2/216x^2+(-576x)/216x^2+324x/216x^2=0

We multiply all the terms by the denominator


84x^2+(-576x)+324x=0

We add all the numbers together, and all the variables

84x^2+324x+(-576x)=0

We get rid of parentheses

84x^2+324x-576x=0

We add all the numbers together, and all the variables

84x^2-252x=0

a = 84; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·84·0
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*84}=\frac{0}{168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*84}=\frac{504}{168}
=3
$