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

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

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

We move all terms to the left:

5/4x-1-(1+5-4x)=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-(-4x+6)-1=0

We get rid of parentheses

5/4x+4x-6-1=0

We multiply all the terms by the denominator


4x*4x-6*4x-1*4x+5=0

Wy multiply elements

16x^2-24x-4x+5=0

We add all the numbers together, and all the variables

16x^2-28x+5=0

a = 16; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·16·5
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{29}}{2*16}=\frac{28-4\sqrt{29}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{29}}{2*16}=\frac{28+4\sqrt{29}}{32}
$