8/x-32x=12

Solution for 8/x-32x=12 equation:

8/x-32x=12

We move all terms to the left:

8/x-32x-(12)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-32x+8/x-12=0

We multiply all the terms by the denominator


-32x*x-12*x+8=0

We add all the numbers together, and all the variables

-12x-32x*x+8=0

Wy multiply elements

-32x^2-12x+8=0

a = -32; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·(-32)·8
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{73}}{2*-32}=\frac{12-4\sqrt{73}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{73}}{2*-32}=\frac{12+4\sqrt{73}}{-64}
$