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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


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

We calculate fractions


256x/64x^2+5x/64x^2+(-x)/64x^2-5=0

We add all the numbers together, and all the variables

256x/64x^2+5x/64x^2+(-1x)/64x^2-5=0

We multiply all the terms by the denominator


256x+5x+(-1x)-5*64x^2=0

We add all the numbers together, and all the variables

261x+(-1x)-5*64x^2=0

Wy multiply elements

-320x^2+261x+(-1x)=0

We get rid of parentheses

-320x^2+261x-1x=0

We add all the numbers together, and all the variables

-320x^2+260x=0

a = -320; b = 260; c = 0;
Δ = b2-4ac
Δ = 2602-4·(-320)·0
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(260)-260}{2*-320}=\frac{-520}{-640}
=13/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(260)+260}{2*-320}=\frac{0}{-640}
=0
$