y-2/2y-4=8

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

y-2/2y-4=8

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y-2/2y-12=0

We multiply all the terms by the denominator


y*2y-12*2y-2=0

Wy multiply elements

2y^2-24y-2=0

a = 2; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·2·(-2)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{37}}{2*2}=\frac{24-4\sqrt{37}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{37}}{2*2}=\frac{24+4\sqrt{37}}{4}
$