x*(1/5x)=80000

Solution for x*(1/5x)=80000 equation:

x(1/5x)=80000

We move all terms to the left:

x(1/5x)-(80000)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+1/5x)-80000=0

We multiply parentheses

x^2-80000=0

a = 1; b = 0; c = -80000;
Δ = b2-4ac
Δ = 02-4·1·(-80000)
Δ = 320000
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:

$\sqrt{\Delta}=\sqrt{320000}=\sqrt{160000*2}=\sqrt{160000}*\sqrt{2}=400\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{2}}{2*1}=\frac{0-400\sqrt{2}}{2}
=-\frac{400\sqrt{2}}{2}
=-200\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{2}}{2*1}=\frac{0+400\sqrt{2}}{2}
=\frac{400\sqrt{2}}{2}
=200\sqrt{2}
$