3/3x-7=2x+3

Solution for 3/3x-7=2x+3 equation:

3/3x-7=2x+3

We move all terms to the left:

3/3x-7-(2x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

3/3x-2x-3-7=0

We multiply all the terms by the denominator


-2x*3x-3*3x-7*3x+3=0

Wy multiply elements

-6x^2-9x-21x+3=0

We add all the numbers together, and all the variables

-6x^2-30x+3=0

a = -6; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·(-6)·3
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{3}}{2*-6}=\frac{30-18\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{3}}{2*-6}=\frac{30+18\sqrt{3}}{-12}
$