2+y2+4y=32

Solution for 2+y2+4y=32 equation:

2+y2+4y=32

We move all terms to the left:

2+y2+4y-(32)=0

We add all the numbers together, and all the variables

y^2+4y-30=0

a = 1; b = 4; c = -30;
Δ = b2-4ac
Δ = 42-4·1·(-30)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{34}}{2*1}=\frac{-4-2\sqrt{34}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{34}}{2*1}=\frac{-4+2\sqrt{34}}{2}
$