320=x+4/5x

Solution for 320=x+4/5x equation:

320=x+4/5x

We move all terms to the left:

320-(x+4/5x)=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+4/5x)+320=0

We get rid of parentheses

-x-4/5x+320=0

We multiply all the terms by the denominator


-x*5x+320*5x-4=0

Wy multiply elements

-5x^2+1600x-4=0

a = -5; b = 1600; c = -4;
Δ = b2-4ac
Δ = 16002-4·(-5)·(-4)
Δ = 2559920
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:

$\sqrt{\Delta}=\sqrt{2559920}=\sqrt{16*159995}=\sqrt{16}*\sqrt{159995}=4\sqrt{159995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-4\sqrt{159995}}{2*-5}=\frac{-1600-4\sqrt{159995}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+4\sqrt{159995}}{2*-5}=\frac{-1600+4\sqrt{159995}}{-10}
$