X=320+1/5x

Solution for X=320+1/5x equation:

X=320+1/5X

We move all terms to the left:

X-(320+1/5X)=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-(1/5X+320)=0

We get rid of parentheses

X-1/5X-320=0

We multiply all the terms by the denominator


X*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}
$