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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


4x/6x^2+9x/6x^2-7-9=0

We add all the numbers together, and all the variables

4x/6x^2+9x/6x^2-16=0

We multiply all the terms by the denominator


4x+9x-16*6x^2=0

We add all the numbers together, and all the variables

13x-16*6x^2=0

Wy multiply elements

-96x^2+13x=0

a = -96; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-96)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-96}=\frac{-26}{-192}
=13/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-96}=\frac{0}{-192}
=0
$