3-1/2x=9-2/3x

Solution for 3-1/2x=9-2/3x equation:

3-1/2x=9-2/3x

We move all terms to the left:

3-1/2x-(9-2/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(-2/3x+9)+3=0

We get rid of parentheses

-1/2x+2/3x-9+3=0

We calculate fractions


(-3x)/6x^2+4x/6x^2-9+3=0

We add all the numbers together, and all the variables

(-3x)/6x^2+4x/6x^2-6=0

We multiply all the terms by the denominator


(-3x)+4x-6*6x^2=0

We add all the numbers together, and all the variables

4x+(-3x)-6*6x^2=0

Wy multiply elements

-36x^2+4x+(-3x)=0

We get rid of parentheses

-36x^2+4x-3x=0

We add all the numbers together, and all the variables

-36x^2+x=0

a = -36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-36)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-36}=\frac{-2}{-72}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-36}=\frac{0}{-72}
=0
$