x-1/5x=8

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

x-1/5x=8

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


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}
$