x=1/5x+8+100

Solution for x=1/5x+8+100 equation:

x=1/5x+8+100

We move all terms to the left:

x-(1/5x+8+100)=0


Domain of the equation: 5x+8+100)!=0

We move all terms containing x to the left, all other terms to the right

5x+100)!=-8

x∈R


We add all the numbers together, and all the variables

x-(1/5x+108)=0

We get rid of parentheses

x-1/5x-108=0

We multiply all the terms by the denominator


x*5x-108*5x-1=0

Wy multiply elements

5x^2-540x-1=0

a = 5; b = -540; c = -1;
Δ = b2-4ac
Δ = -5402-4·5·(-1)
Δ = 291620
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:

$\sqrt{\Delta}=\sqrt{291620}=\sqrt{4*72905}=\sqrt{4}*\sqrt{72905}=2\sqrt{72905}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72905}}{2*5}=\frac{540-2\sqrt{72905}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72905}}{2*5}=\frac{540+2\sqrt{72905}}{10}
$