2x+800/x=80x

Solution for 2x+800/x=80x equation:

2x+800/x=80x

We move all terms to the left:

2x+800/x-(80x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-78x+800/x=0

We multiply all the terms by the denominator


-78x*x+800=0

Wy multiply elements

-78x^2+800=0

a = -78; b = 0; c = +800;
Δ = b2-4ac
Δ = 02-4·(-78)·800
Δ = 249600
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:

$\sqrt{\Delta}=\sqrt{249600}=\sqrt{6400*39}=\sqrt{6400}*\sqrt{39}=80\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{39}}{2*-78}=\frac{0-80\sqrt{39}}{-156}
=-\frac{80\sqrt{39}}{-156}
=-\frac{20\sqrt{39}}{-39}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{39}}{2*-78}=\frac{0+80\sqrt{39}}{-156}
=\frac{80\sqrt{39}}{-156}
=\frac{20\sqrt{39}}{-39}
$