y-1/2y=16

Solution for y-1/2y=16 equation:

y-1/2y=16

We move all terms to the left:

y-1/2y-(16)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


y*2y-16*2y-1=0

Wy multiply elements

2y^2-32y-1=0

a = 2; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·2·(-1)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{258}}{2*2}=\frac{32-2\sqrt{258}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{258}}{2*2}=\frac{32+2\sqrt{258}}{4}
$