-4/2x-9=-16/3x+14

Solution for -4/2x-9=-16/3x+14 equation:

-4/2x-9=-16/3x+14

We move all terms to the left:

-4/2x-9-(-16/3x+14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+14)!=0

x∈R


We get rid of parentheses

-4/2x+16/3x-14-9=0

We calculate fractions


(-12x)/6x^2+32x/6x^2-14-9=0

We add all the numbers together, and all the variables

(-12x)/6x^2+32x/6x^2-23=0

We multiply all the terms by the denominator


(-12x)+32x-23*6x^2=0

We add all the numbers together, and all the variables

32x+(-12x)-23*6x^2=0

Wy multiply elements

-138x^2+32x+(-12x)=0

We get rid of parentheses

-138x^2+32x-12x=0

We add all the numbers together, and all the variables

-138x^2+20x=0

a = -138; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-138)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-138}=\frac{-40}{-276}
=10/69
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-138}=\frac{0}{-276}
=0
$