3x-7=1/3x+3

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

3x-7=1/3x+3

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2-9x-21x-1=0

We add all the numbers together, and all the variables

9x^2-30x-1=0

a = 9; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·9·(-1)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{26}}{2*9}=\frac{30-6\sqrt{26}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{26}}{2*9}=\frac{30+6\sqrt{26}}{18}
$