3x-1=7/3x+3

Solution for 3x-1=7/3x+3 equation:

3x-1=7/3x+3

We move all terms to the left:

3x-1-(7/3x+3)=0


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

x∈R


We get rid of parentheses

3x-7/3x-3-1=0

We multiply all the terms by the denominator


3x*3x-3*3x-1*3x-7=0

Wy multiply elements

9x^2-9x-3x-7=0

We add all the numbers together, and all the variables

9x^2-12x-7=0

a = 9; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·9·(-7)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{11}}{2*9}=\frac{12-6\sqrt{11}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{11}}{2*9}=\frac{12+6\sqrt{11}}{18}
$