1/x+5/4x=1/2

Solution for 1/x+5/4x=1/2 equation:

1/x+5/4x=1/2

We move all terms to the left:

1/x+5/4x-(1/2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/x+5/4x-(+1/2)=0

We get rid of parentheses

1/x+5/4x-1/2=0

We calculate fractions


(-16x^2)/16x^2+16x/16x^2+20x/16x^2=0

We multiply all the terms by the denominator


(-16x^2)+16x+20x=0

We add all the numbers together, and all the variables

(-16x^2)+36x=0

We get rid of parentheses

-16x^2+36x=0

a = -16; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-16)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-16}=\frac{-72}{-32}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-16}=\frac{0}{-32}
=0
$