x-4/5x=1/5x+1

Solution for x-4/5x=1/5x+1 equation:

x-4/5x=1/5x+1

We move all terms to the left:

x-4/5x-(1/5x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

x-4/5x-1/5x-1=0

We multiply all the terms by the denominator


x*5x-1*5x-4-1=0

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-5x-5=0

a = 5; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·5·(-5)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{5}}{2*5}=\frac{5-5\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{5}}{2*5}=\frac{5+5\sqrt{5}}{10}
$