4-2/9x=1/3x-7

Solution for 4-2/9x=1/3x-7 equation:

4-2/9x=1/3x-7

We move all terms to the left:

4-2/9x-(1/3x-7)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

-2/9x-1/3x+7+4=0

We calculate fractions


(-6x)/27x^2+(-9x)/27x^2+7+4=0

We add all the numbers together, and all the variables

(-6x)/27x^2+(-9x)/27x^2+11=0

We multiply all the terms by the denominator


(-6x)+(-9x)+11*27x^2=0

Wy multiply elements

297x^2+(-6x)+(-9x)=0

We get rid of parentheses

297x^2-6x-9x=0

We add all the numbers together, and all the variables

297x^2-15x=0

a = 297; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·297·0
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*297}=\frac{0}{594}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*297}=\frac{30}{594}
=5/99
$