1/4y-4y^-1=0

Solution for 1/4y-4y^-1=0 equation:

1/4y-4y^-1=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-4y+1/4y-1=0

We multiply all the terms by the denominator


-4y*4y-1*4y+1=0

Wy multiply elements

-16y^2-4y+1=0

a = -16; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-16)·1
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*-16}=\frac{4-4\sqrt{5}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*-16}=\frac{4+4\sqrt{5}}{-32}
$