3x-3/3x-9=4

Solution for 3x-3/3x-9=4 equation:

3x-3/3x-9=4

We move all terms to the left:

3x-3/3x-9-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x-3/3x-13=0

We multiply all the terms by the denominator


3x*3x-13*3x-3=0

Wy multiply elements

9x^2-39x-3=0

a = 9; b = -39; c = -3;
Δ = b2-4ac
Δ = -392-4·9·(-3)
Δ = 1629
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1629}=\sqrt{9*181}=\sqrt{9}*\sqrt{181}=3\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{181}}{2*9}=\frac{39-3\sqrt{181}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{181}}{2*9}=\frac{39+3\sqrt{181}}{18}
$