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

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

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

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2+4x-20x-1=0

We add all the numbers together, and all the variables

16x^2-16x-1=0

a = 16; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·16·(-1)
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{-(-16)-8\sqrt{5}}{2*16}=\frac{16-8\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{5}}{2*16}=\frac{16+8\sqrt{5}}{32}
$