8x-3000*1/x=0

Solution for 8x-3000*1/x=0 equation:

8x-3000*1/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


8x*x-3000*1=0

We add all the numbers together, and all the variables

8x*x-3000=0

Wy multiply elements

8x^2-3000=0

a = 8; b = 0; c = -3000;
Δ = b2-4ac
Δ = 02-4·8·(-3000)
Δ = 96000
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:

$\sqrt{\Delta}=\sqrt{96000}=\sqrt{6400*15}=\sqrt{6400}*\sqrt{15}=80\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{15}}{2*8}=\frac{0-80\sqrt{15}}{16}
=-\frac{80\sqrt{15}}{16}
=-5\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{15}}{2*8}=\frac{0+80\sqrt{15}}{16}
=\frac{80\sqrt{15}}{16}
=5\sqrt{15}
$