y^2+2y=16

Solution for y^2+2y=16 equation:

y^2+2y=16

We move all terms to the left:

y^2+2y-(16)=0

a = 1; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·1·(-16)
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{-(2)-2\sqrt{17}}{2*1}=\frac{-2-2\sqrt{17}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{17}}{2*1}=\frac{-2+2\sqrt{17}}{2}
$