y^2-4y-1=32

Solution for y^2-4y-1=32 equation:

y^2-4y-1=32

We move all terms to the left:

y^2-4y-1-(32)=0

We add all the numbers together, and all the variables

y^2-4y-33=0

a = 1; b = -4; c = -33;
Δ = b2-4ac
Δ = -42-4·1·(-33)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{37}}{2*1}=\frac{4-2\sqrt{37}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{37}}{2*1}=\frac{4+2\sqrt{37}}{2}
$