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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+16)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-8x)/12x^2+(-9x)/12x^2-16-9=0

We add all the numbers together, and all the variables

(-8x)/12x^2+(-9x)/12x^2-25=0

We multiply all the terms by the denominator


(-8x)+(-9x)-25*12x^2=0

Wy multiply elements

-300x^2+(-8x)+(-9x)=0

We get rid of parentheses

-300x^2-8x-9x=0

We add all the numbers together, and all the variables

-300x^2-17x=0

a = -300; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-300)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-300}=\frac{0}{-600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-300}=\frac{34}{-600}
=-17/300
$