8x-3/x=3

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

8x-3/x=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

8x^2-3x-3=0

a = 8; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·8·(-3)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{105}}{2*8}=\frac{3-\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*8}=\frac{3+\sqrt{105}}{16}
$