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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


144x^2/48x^2+(-64x)/48x^2+60x/48x^2-5=0

We multiply all the terms by the denominator


144x^2+(-64x)+60x-5*48x^2=0

We add all the numbers together, and all the variables

144x^2+60x+(-64x)-5*48x^2=0

Wy multiply elements

144x^2-240x^2+60x+(-64x)=0

We get rid of parentheses

144x^2-240x^2+60x-64x=0

We add all the numbers together, and all the variables

-96x^2-4x=0

a = -96; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-96)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-96}=\frac{8}{-192}
=-1/24
$