-3/2x+9=4/3x-3

Solution for -3/2x+9=4/3x-3 equation:

-3/2x+9=4/3x-3

We move all terms to the left:

-3/2x+9-(4/3x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

-3/2x-4/3x+3+9=0

We calculate fractions


(-9x)/6x^2+(-8x)/6x^2+3+9=0

We add all the numbers together, and all the variables

(-9x)/6x^2+(-8x)/6x^2+12=0

We multiply all the terms by the denominator


(-9x)+(-8x)+12*6x^2=0

Wy multiply elements

72x^2+(-9x)+(-8x)=0

We get rid of parentheses

72x^2-9x-8x=0

We add all the numbers together, and all the variables

72x^2-17x=0

a = 72; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·72·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*72}=\frac{34}{144}
=17/72
$