1/5x-x=320

Solution for 1/5x-x=320 equation:

1/5x-x=320

We move all terms to the left:

1/5x-x-(320)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/5x-320=0

We multiply all the terms by the denominator


-1x*5x-320*5x+1=0

Wy multiply elements

-5x^2-1600x+1=0

a = -5; b = -1600; c = +1;
Δ = b2-4ac
Δ = -16002-4·(-5)·1
Δ = 2560020
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:

$\sqrt{\Delta}=\sqrt{2560020}=\sqrt{4*640005}=\sqrt{4}*\sqrt{640005}=2\sqrt{640005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1600)-2\sqrt{640005}}{2*-5}=\frac{1600-2\sqrt{640005}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1600)+2\sqrt{640005}}{2*-5}=\frac{1600+2\sqrt{640005}}{-10}
$