y2+6Y+16X+41=0

Solution for y2+6Y+16X+41=0 equation:

y2+6+16y+41=0

We add all the numbers together, and all the variables

y^2+16y+47=0

a = 1; b = 16; c = +47;
Δ = b2-4ac
Δ = 162-4·1·47
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{17}}{2*1}=\frac{-16-2\sqrt{17}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{17}}{2*1}=\frac{-16+2\sqrt{17}}{2}
$