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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2+16x-6=0

a = 4; b = 16; c = -6;
Δ = b2-4ac
Δ = 162-4·4·(-6)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{22}}{2*4}=\frac{-16-4\sqrt{22}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{22}}{2*4}=\frac{-16+4\sqrt{22}}{8}
$