1/1x+1/4x=16

Solution for 1/1x+1/4x=16 equation:

1/1x+1/4x=16

We move all terms to the left:

1/1x+1/4x-(16)=0


Domain of the equation: 1x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/4x^2+x/4x^2-16=0

We multiply all the terms by the denominator


4x+x-16*4x^2=0

We add all the numbers together, and all the variables

5x-16*4x^2=0

Wy multiply elements

-64x^2+5x=0

a = -64; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-64)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-64}=\frac{-10}{-128}
=5/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-64}=\frac{0}{-128}
=0
$