3/4x+4/9+1/3x=289/36

Solution for 3/4x+4/9+1/3x=289/36 equation:

3/4x+4/9+1/3x=289/36

We move all terms to the left:

3/4x+4/9+1/3x-(289/36)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+1/3x+4/9-(+289/36)=0

We get rid of parentheses

3/4x+1/3x+4/9-289/36=0

We calculate fractions


(-93636x^2)/34992x^2+5184x^2/34992x^2+26244x/34992x^2+11664x/34992x^2=0

We multiply all the terms by the denominator


(-93636x^2)+5184x^2+26244x+11664x=0

We add all the numbers together, and all the variables

5184x^2+(-93636x^2)+37908x=0

We get rid of parentheses

5184x^2-93636x^2+37908x=0

We add all the numbers together, and all the variables

-88452x^2+37908x=0

a = -88452; b = 37908; c = 0;
Δ = b2-4ac
Δ = 379082-4·(-88452)·0
Δ = 1437016464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1437016464}=37908$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37908)-37908}{2*-88452}=\frac{-75816}{-176904}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37908)+37908}{2*-88452}=\frac{0}{-176904}
=0
$