4x-5=1/5x

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

4x-5=1/5x

We move all terms to the left:

4x-5-(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

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

We get rid of parentheses

4x-1/5x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-25x-1=0

a = 20; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·20·(-1)
Δ = 705
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{-(-25)-\sqrt{705}}{2*20}=\frac{25-\sqrt{705}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{705}}{2*20}=\frac{25+\sqrt{705}}{40}
$