-4x+5000/x=0

Solution for -4x+5000/x=0 equation:

-4x+5000/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-4x*x+5000=0

Wy multiply elements

-4x^2+5000=0

a = -4; b = 0; c = +5000;
Δ = b2-4ac
Δ = 02-4·(-4)·5000
Δ = 80000
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:

$\sqrt{\Delta}=\sqrt{80000}=\sqrt{40000*2}=\sqrt{40000}*\sqrt{2}=200\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{2}}{2*-4}=\frac{0-200\sqrt{2}}{-8}
=-\frac{200\sqrt{2}}{-8}
=-\frac{25\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{2}}{2*-4}=\frac{0+200\sqrt{2}}{-8}
=\frac{200\sqrt{2}}{-8}
=\frac{25\sqrt{2}}{-1}
$