6-2/9x+(-3)=1/3x+4

Solution for 6-2/9x+(-3)=1/3x+4 equation:

6-2/9x+(-3)=1/3x+4

We move all terms to the left:

6-2/9x+(-3)-(1/3x+4)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-6x)/27x^2+(-9x)/27x^2-4+3=0

We add all the numbers together, and all the variables

(-6x)/27x^2+(-9x)/27x^2-1=0

We multiply all the terms by the denominator


(-6x)+(-9x)-1*27x^2=0

Wy multiply elements

-27x^2+(-6x)+(-9x)=0

We get rid of parentheses

-27x^2-6x-9x=0

We add all the numbers together, and all the variables

-27x^2-15x=0

a = -27; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-27)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-27}=\frac{0}{-54}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-27}=\frac{30}{-54}
=-5/9
$