-5/2x-9-9/3x-5=6

Solution for -5/2x-9-9/3x-5=6 equation:

-5/2x-9-9/3x-5=6

We move all terms to the left:

-5/2x-9-9/3x-5-(6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-5/2x-9/3x-20=0

We calculate fractions


(-15x)/6x^2+(-18x)/6x^2-20=0

We multiply all the terms by the denominator


(-15x)+(-18x)-20*6x^2=0

Wy multiply elements

-120x^2+(-15x)+(-18x)=0

We get rid of parentheses

-120x^2-15x-18x=0

We add all the numbers together, and all the variables

-120x^2-33x=0

a = -120; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·(-120)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*-120}=\frac{66}{-240}
=-11/40
$