y^2+64y-1024=0

Solution for y^2+64y-1024=0 equation:

y^2+64y-1024=0

a = 1; b = 64; c = -1024;
Δ = b2-4ac
Δ = 642-4·1·(-1024)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64\sqrt{2}}{2*1}=\frac{-64-64\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64\sqrt{2}}{2*1}=\frac{-64+64\sqrt{2}}{2}
$