-1/2x+9=4/3x-3

Solution for -1/2x+9=4/3x-3 equation:

-1/2x+9=4/3x-3

We move all terms to the left:

-1/2x+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

-1/2x-4/3x+3+9=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-3x)/6x^2+(-8x)/6x^2+12=0

We multiply all the terms by the denominator


(-3x)+(-8x)+12*6x^2=0

Wy multiply elements

72x^2+(-3x)+(-8x)=0

We get rid of parentheses

72x^2-3x-8x=0

We add all the numbers together, and all the variables

72x^2-11x=0

a = 72; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·72·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*72}=\frac{22}{144}
=11/72
$