3x+6/2x-4=3

Solution for 3x+6/2x-4=3 equation:

3x+6/2x-4=3

We move all terms to the left:

3x+6/2x-4-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+6/2x-7=0

We multiply all the terms by the denominator


3x*2x-7*2x+6=0

Wy multiply elements

6x^2-14x+6=0

a = 6; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·6·6
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{13}}{2*6}=\frac{14-2\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{13}}{2*6}=\frac{14+2\sqrt{13}}{12}
$