y^2-16y+61=0

Solution for y^2-16y+61=0 equation:

y^2-16y+61=0

a = 1; b = -16; c = +61;
Δ = b2-4ac
Δ = -162-4·1·61
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{3}}{2*1}=\frac{16-2\sqrt{3}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{3}}{2*1}=\frac{16+2\sqrt{3}}{2}
$