-3/2x-7/3x=23/9

Solution for -3/2x-7/3x=23/9 equation:

-3/2x-7/3x=23/9

We move all terms to the left:

-3/2x-7/3x-(23/9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-7/3x-(+23/9)=0

We get rid of parentheses

-3/2x-7/3x-23/9=0

We calculate fractions


(-414x^2)/486x^2+(-729x)/486x^2+(-1134x)/486x^2=0

We multiply all the terms by the denominator


(-414x^2)+(-729x)+(-1134x)=0

We get rid of parentheses

-414x^2-729x-1134x=0

We add all the numbers together, and all the variables

-414x^2-1863x=0

a = -414; b = -1863; c = 0;
Δ = b2-4ac
Δ = -18632-4·(-414)·0
Δ = 3470769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3470769}=1863$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1863)-1863}{2*-414}=\frac{0}{-828}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1863)+1863}{2*-414}=\frac{3726}{-828}
=-4+1/2
$