X^2-66x+684=0

Solution for X^2-66x+684=0 equation:

X^2-66X+684=0

a = 1; b = -66; c = +684;
Δ = b2-4ac
Δ = -662-4·1·684
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-18\sqrt{5}}{2*1}=\frac{66-18\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+18\sqrt{5}}{2*1}=\frac{66+18\sqrt{5}}{2}
$