X2-64x-768=0

Solution for X2-64x-768=0 equation:

X2-64X-768=0

We add all the numbers together, and all the variables

X^2-64X-768=0

a = 1; b = -64; c = -768;
Δ = b2-4ac
Δ = -642-4·1·(-768)
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32\sqrt{7}}{2*1}=\frac{64-32\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{7}}{2*1}=\frac{64+32\sqrt{7}}{2}
$