x+8=1/5x

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

x+8=1/5x

We move all terms to the left:

x+8-(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)+8=0

We get rid of parentheses

x-1/5x+8=0

We multiply all the terms by the denominator


x*5x+8*5x-1=0

Wy multiply elements

5x^2+40x-1=0

a = 5; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·5·(-1)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-18\sqrt{5}}{2*5}=\frac{-40-18\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+18\sqrt{5}}{2*5}=\frac{-40+18\sqrt{5}}{10}
$