2/3x-3/4+9/4x+1/3=2

Solution for 2/3x-3/4+9/4x+1/3=2 equation:

2/3x-3/4+9/4x+1/3=2

We move all terms to the left:

2/3x-3/4+9/4x+1/3-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


determiningTheFunctionDomain
2/3x+9/4x-2-3/4+1/3=0

We calculate fractions


128x/576x^2+243x/576x^2+(-81x)/576x^2+64x/576x^2-2=0

We multiply all the terms by the denominator


128x+243x+(-81x)+64x-2*576x^2=0

We add all the numbers together, and all the variables

435x+(-81x)-2*576x^2=0

Wy multiply elements

-1152x^2+435x+(-81x)=0

We get rid of parentheses

-1152x^2+435x-81x=0

We add all the numbers together, and all the variables

-1152x^2+354x=0

a = -1152; b = 354; c = 0;
Δ = b2-4ac
Δ = 3542-4·(-1152)·0
Δ = 125316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{125316}=354$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(354)-354}{2*-1152}=\frac{-708}{-2304}
=59/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(354)+354}{2*-1152}=\frac{0}{-2304}
=0
$