y2+16y=2

Solution for y2+16y=2 equation:

y2+16y=2

We move all terms to the left:

y2+16y-(2)=0

We add all the numbers together, and all the variables

y^2+16y-2=0

a = 1; b = 16; c = -2;
Δ = b2-4ac
Δ = 162-4·1·(-2)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{66}}{2*1}=\frac{-16-2\sqrt{66}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{66}}{2*1}=\frac{-16+2\sqrt{66}}{2}
$