5/4x-1=1+54x

Solution for 5/4x-1=1+54x equation:

5/4x-1=1+54x

We move all terms to the left:

5/4x-1-(1+54x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(54x+1)-1=0

We get rid of parentheses

5/4x-54x-1-1=0

We multiply all the terms by the denominator


-54x*4x-1*4x-1*4x+5=0

Wy multiply elements

-216x^2-4x-4x+5=0

We add all the numbers together, and all the variables

-216x^2-8x+5=0

a = -216; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·(-216)·5
Δ = 4384
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:

$\sqrt{\Delta}=\sqrt{4384}=\sqrt{16*274}=\sqrt{16}*\sqrt{274}=4\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{274}}{2*-216}=\frac{8-4\sqrt{274}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{274}}{2*-216}=\frac{8+4\sqrt{274}}{-432}
$