6x-12=208/x

Solution for 6x-12=208/x equation:

6x-12=208/x

We move all terms to the left:

6x-12-(208/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+208/x)-12=0

We get rid of parentheses

6x-208/x-12=0

We multiply all the terms by the denominator


6x*x-12*x-208=0

We add all the numbers together, and all the variables

-12x+6x*x-208=0

Wy multiply elements

6x^2-12x-208=0

a = 6; b = -12; c = -208;
Δ = b2-4ac
Δ = -122-4·6·(-208)
Δ = 5136
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:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{321}}{2*6}=\frac{12-4\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{321}}{2*6}=\frac{12+4\sqrt{321}}{12}
$