3/2x-10=12/x+9

Solution for 3/2x-10=12/x+9 equation:

3/2x-10=12/x+9

We move all terms to the left:

3/2x-10-(12/x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+9)!=0

x∈R


We get rid of parentheses

3/2x-12/x-9-10=0

We calculate fractions


3x/2x^2+(-24x)/2x^2-9-10=0

We add all the numbers together, and all the variables

3x/2x^2+(-24x)/2x^2-19=0

We multiply all the terms by the denominator


3x+(-24x)-19*2x^2=0

Wy multiply elements

-38x^2+3x+(-24x)=0

We get rid of parentheses

-38x^2+3x-24x=0

We add all the numbers together, and all the variables

-38x^2-21x=0

a = -38; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-38)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-38}=\frac{0}{-76}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-38}=\frac{42}{-76}
=-21/38
$