X^2-66x-1225=0

Solution for X^2-66x-1225=0 equation:

X^2-66X-1225=0

a = 1; b = -66; c = -1225;
Δ = b2-4ac
Δ = -662-4·1·(-1225)
Δ = 9256
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:

$\sqrt{\Delta}=\sqrt{9256}=\sqrt{4*2314}=\sqrt{4}*\sqrt{2314}=2\sqrt{2314}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{2314}}{2*1}=\frac{66-2\sqrt{2314}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{2314}}{2*1}=\frac{66+2\sqrt{2314}}{2}
$