5x=78125/x

Solution for 5x=78125/x equation:

5x=78125/x

We move all terms to the left:

5x-(78125/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+78125/x)=0

We get rid of parentheses

5x-78125/x=0

We multiply all the terms by the denominator


5x*x-78125=0

Wy multiply elements

5x^2-78125=0

a = 5; b = 0; c = -78125;
Δ = b2-4ac
Δ = 02-4·5·(-78125)
Δ = 1562500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1562500}=1250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1250}{2*5}=\frac{-1250}{10}
=-125
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1250}{2*5}=\frac{1250}{10}
=125
$