x^2-3x-255=0

Solution for x^2-3x-255=0 equation:

x^2-3x-255=0

a = 1; b = -3; c = -255;
Δ = b2-4ac
Δ = -32-4·1·(-255)
Δ = 1029
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:

$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7\sqrt{21}}{2*1}=\frac{3-7\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7\sqrt{21}}{2*1}=\frac{3+7\sqrt{21}}{2}
$