x=99+1/5x

Solution for x=99+1/5x equation:

x=99+1/5x

We move all terms to the left:

x-(99+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+99)=0

We get rid of parentheses

x-1/5x-99=0

We multiply all the terms by the denominator


x*5x-99*5x-1=0

Wy multiply elements

5x^2-495x-1=0

a = 5; b = -495; c = -1;
Δ = b2-4ac
Δ = -4952-4·5·(-1)
Δ = 245045
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-495)-\sqrt{245045}}{2*5}=\frac{495-\sqrt{245045}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-495)+\sqrt{245045}}{2*5}=\frac{495+\sqrt{245045}}{10}
$