8x-2=12/x

Solution for 8x-2=12/x equation:

8x-2=12/x

We move all terms to the left:

8x-2-(12/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

8x-(+12/x)-2=0

We get rid of parentheses

8x-12/x-2=0

We multiply all the terms by the denominator


8x*x-2*x-12=0

We add all the numbers together, and all the variables

-2x+8x*x-12=0

Wy multiply elements

8x^2-2x-12=0

a = 8; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·8·(-12)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{97}}{2*8}=\frac{2-2\sqrt{97}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{97}}{2*8}=\frac{2+2\sqrt{97}}{16}
$