2/6x+1=3x-5

Solution for 2/6x+1=3x-5 equation:

2/6x+1=3x-5

We move all terms to the left:

2/6x+1-(3x-5)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

2/6x-3x+5+1=0

We multiply all the terms by the denominator


-3x*6x+5*6x+1*6x+2=0

Wy multiply elements

-18x^2+30x+6x+2=0

We add all the numbers together, and all the variables

-18x^2+36x+2=0

a = -18; b = 36; c = +2;
Δ = b2-4ac
Δ = 362-4·(-18)·2
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{10}}{2*-18}=\frac{-36-12\sqrt{10}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{10}}{2*-18}=\frac{-36+12\sqrt{10}}{-36}
$