8*1-2y=1/4y

Solution for 8*1-2y=1/4y equation:

8*1-2y=1/4y

We move all terms to the left:

8*1-2y-(1/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-2y-(+1/4y)+8*1=0

We add all the numbers together, and all the variables

-2y-(+1/4y)+8=0

We get rid of parentheses

-2y-1/4y+8=0

We multiply all the terms by the denominator


-2y*4y+8*4y-1=0

Wy multiply elements

-8y^2+32y-1=0

a = -8; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·(-8)·(-1)
Δ = 992
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:

$\sqrt{\Delta}=\sqrt{992}=\sqrt{16*62}=\sqrt{16}*\sqrt{62}=4\sqrt{62}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{62}}{2*-8}=\frac{-32-4\sqrt{62}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{62}}{2*-8}=\frac{-32+4\sqrt{62}}{-16}
$