y^2-24y+64=0

Solution for y^2-24y+64=0 equation:

y^2-24y+64=0

a = 1; b = -24; c = +64;
Δ = b2-4ac
Δ = -242-4·1·64
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{5}}{2*1}=\frac{24-8\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{5}}{2*1}=\frac{24+8\sqrt{5}}{2}
$