8x-3/x=12

Solution for 8x-3/x=12 equation:

8x-3/x=12

We move all terms to the left:

8x-3/x-(12)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


8x*x-12*x-3=0

We add all the numbers together, and all the variables

-12x+8x*x-3=0

Wy multiply elements

8x^2-12x-3=0

a = 8; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·8·(-3)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*8}=\frac{12-4\sqrt{15}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*8}=\frac{12+4\sqrt{15}}{16}
$