y2+64y-1536=0

Solution for y2+64y-1536=0 equation:

y2+64y-1536=0

We add all the numbers together, and all the variables

y^2+64y-1536=0

a = 1; b = 64; c = -1536;
Δ = b2-4ac
Δ = 642-4·1·(-1536)
Δ = 10240
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:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-32\sqrt{10}}{2*1}=\frac{-64-32\sqrt{10}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+32\sqrt{10}}{2*1}=\frac{-64+32\sqrt{10}}{2}
$