6/3x+12/2x=1

Solution for 6/3x+12/2x=1 equation:

6/3x+12/2x=1

We move all terms to the left:

6/3x+12/2x-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


12x/6x^2+36x/6x^2-1=0

We multiply all the terms by the denominator


12x+36x-1*6x^2=0

We add all the numbers together, and all the variables

48x-1*6x^2=0

Wy multiply elements

-6x^2+48x=0

a = -6; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-6)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-6}=\frac{-96}{-12}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-6}=\frac{0}{-12}
=0
$