20x=10x+80/x=400

Solution for 20x=10x+80/x=400 equation:

20x=10x+80/x=400

We move all terms to the left:

20x-(10x+80/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

20x-(+10x+80/x)=0

We get rid of parentheses

20x-10x-80/x=0

We multiply all the terms by the denominator


20x*x-10x*x-80=0

Wy multiply elements

20x^2-10x^2-80=0

We add all the numbers together, and all the variables

10x^2-80=0

a = 10; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·10·(-80)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*10}=\frac{0-40\sqrt{2}}{20}
=-\frac{40\sqrt{2}}{20}
=-2\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*10}=\frac{0+40\sqrt{2}}{20}
=\frac{40\sqrt{2}}{20}
=2\sqrt{2}
$