3x=6/2x-3

Solution for 3x=6/2x-3 equation:

3x=6/2x-3

We move all terms to the left:

3x-(6/2x-3)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

3x-6/2x+3=0

We multiply all the terms by the denominator


3x*2x+3*2x-6=0

Wy multiply elements

6x^2+6x-6=0

a = 6; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·6·(-6)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*6}=\frac{-6-6\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*6}=\frac{-6+6\sqrt{5}}{12}
$