3x-3=-4/3x-22

Solution for 3x-3=-4/3x-22 equation:

3x-3=-4/3x-22

We move all terms to the left:

3x-3-(-4/3x-22)=0


Domain of the equation: 3x-22)!=0

x∈R


We get rid of parentheses

3x+4/3x+22-3=0

We multiply all the terms by the denominator


3x*3x+22*3x-3*3x+4=0

Wy multiply elements

9x^2+66x-9x+4=0

We add all the numbers together, and all the variables

9x^2+57x+4=0

a = 9; b = 57; c = +4;
Δ = b2-4ac
Δ = 572-4·9·4
Δ = 3105
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:

$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{345}}{2*9}=\frac{-57-3\sqrt{345}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{345}}{2*9}=\frac{-57+3\sqrt{345}}{18}
$