1/6x=2x+33

Solution for 1/6x=2x+33 equation:

1/6x=2x+33

We move all terms to the left:

1/6x-(2x+33)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

1/6x-2x-33=0

We multiply all the terms by the denominator


-2x*6x-33*6x+1=0

Wy multiply elements

-12x^2-198x+1=0

a = -12; b = -198; c = +1;
Δ = b2-4ac
Δ = -1982-4·(-12)·1
Δ = 39252
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:

$\sqrt{\Delta}=\sqrt{39252}=\sqrt{4*9813}=\sqrt{4}*\sqrt{9813}=2\sqrt{9813}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9813}}{2*-12}=\frac{198-2\sqrt{9813}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9813}}{2*-12}=\frac{198+2\sqrt{9813}}{-24}
$