6x=1/2x+33

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

6x=1/2x+33

We move all terms to the left:

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


Domain of the equation: 2x+33)!=0

x∈R


We get rid of parentheses

6x-1/2x-33=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-66x-1=0

a = 12; b = -66; c = -1;
Δ = b2-4ac
Δ = -662-4·12·(-1)
Δ = 4404
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:

$\sqrt{\Delta}=\sqrt{4404}=\sqrt{4*1101}=\sqrt{4}*\sqrt{1101}=2\sqrt{1101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1101}}{2*12}=\frac{66-2\sqrt{1101}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1101}}{2*12}=\frac{66+2\sqrt{1101}}{24}
$