-9/4x-5=2/3x

Solution for -9/4x-5=2/3x equation:

-9/4x-5=2/3x

We move all terms to the left:

-9/4x-5-(2/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-9/4x-(+2/3x)-5=0

We get rid of parentheses

-9/4x-2/3x-5=0

We calculate fractions


(-27x)/12x^2+(-8x)/12x^2-5=0

We multiply all the terms by the denominator


(-27x)+(-8x)-5*12x^2=0

Wy multiply elements

-60x^2+(-27x)+(-8x)=0

We get rid of parentheses

-60x^2-27x-8x=0

We add all the numbers together, and all the variables

-60x^2-35x=0

a = -60; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-60)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-60}=\frac{70}{-120}
=-7/12
$