5x-4/4x+1=1

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

5x-4/4x+1=1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x-4/4x=0

We multiply all the terms by the denominator


5x*4x-4=0

Wy multiply elements

20x^2-4=0

a = 20; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·20·(-4)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*20}=\frac{0-8\sqrt{5}}{40}
=-\frac{8\sqrt{5}}{40}
=-\frac{\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*20}=\frac{0+8\sqrt{5}}{40}
=\frac{8\sqrt{5}}{40}
=\frac{\sqrt{5}}{5}
$