x^2-64x-2304=0

Solution for x^2-64x-2304=0 equation:

x^2-64x-2304=0

a = 1; b = -64; c = -2304;
Δ = b2-4ac
Δ = -642-4·1·(-2304)
Δ = 13312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13312}=\sqrt{1024*13}=\sqrt{1024}*\sqrt{13}=32\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32\sqrt{13}}{2*1}=\frac{64-32\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{13}}{2*1}=\frac{64+32\sqrt{13}}{2}
$