3/4x+6=9-2/3x

Solution for 3/4x+6=9-2/3x equation:

3/4x+6=9-2/3x

We move all terms to the left:

3/4x+6-(9-2/3x)=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

3/4x-(-2/3x+9)+6=0

We get rid of parentheses

3/4x+2/3x-9+6=0

We calculate fractions


9x/12x^2+8x/12x^2-9+6=0

We add all the numbers together, and all the variables

9x/12x^2+8x/12x^2-3=0

We multiply all the terms by the denominator


9x+8x-3*12x^2=0

We add all the numbers together, and all the variables

17x-3*12x^2=0

Wy multiply elements

-36x^2+17x=0

a = -36; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-36)·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*-36}=\frac{-34}{-72}
=17/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-36}=\frac{0}{-72}
=0
$