y^2-16y-65=100

Solution for y^2-16y-65=100 equation:

y^2-16y-65=100

We move all terms to the left:

y^2-16y-65-(100)=0

We add all the numbers together, and all the variables

y^2-16y-165=0

a = 1; b = -16; c = -165;
Δ = b2-4ac
Δ = -162-4·1·(-165)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{229}}{2*1}=\frac{16-2\sqrt{229}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{229}}{2*1}=\frac{16+2\sqrt{229}}{2}
$