X^2-78x+1009=0

Solution for X^2-78x+1009=0 equation:

X^2-78X+1009=0

a = 1; b = -78; c = +1009;
Δ = b2-4ac
Δ = -782-4·1·1009
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-32\sqrt{2}}{2*1}=\frac{78-32\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+32\sqrt{2}}{2*1}=\frac{78+32\sqrt{2}}{2}
$