x/6x+3=2x+11

Solution for x/6x+3=2x+11 equation:

x/6x+3=2x+11

We move all terms to the left:

x/6x+3-(2x+11)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

x/6x-2x-11+3=0

We multiply all the terms by the denominator


x-2x*6x-11*6x+3*6x=0

Wy multiply elements

-12x^2+x-66x+18x=0

We add all the numbers together, and all the variables

-12x^2-47x=0

a = -12; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·(-12)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*-12}=\frac{94}{-24}
=-3+11/12
$