2x+3=1+4/6x

Solution for 2x+3=1+4/6x equation:

2x+3=1+4/6x

We move all terms to the left:

2x+3-(1+4/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(4/6x+1)+3=0

We get rid of parentheses

2x-4/6x-1+3=0

We multiply all the terms by the denominator


2x*6x-1*6x+3*6x-4=0

Wy multiply elements

12x^2-6x+18x-4=0

We add all the numbers together, and all the variables

12x^2+12x-4=0

a = 12; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·12·(-4)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*12}=\frac{-12-4\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*12}=\frac{-12+4\sqrt{21}}{24}
$