y2-16y+51=0

Solution for y2-16y+51=0 equation:

y2-16y+51=0

We add all the numbers together, and all the variables

y^2-16y+51=0

a = 1; b = -16; c = +51;
Δ = b2-4ac
Δ = -162-4·1·51
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{13}}{2*1}=\frac{16-2\sqrt{13}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{13}}{2*1}=\frac{16+2\sqrt{13}}{2}
$