X^2-4x-254=0

Solution for X^2-4x-254=0 equation:

X^2-4X-254=0

a = 1; b = -4; c = -254;
Δ = b2-4ac
Δ = -42-4·1·(-254)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{258}}{2*1}=\frac{4-2\sqrt{258}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{258}}{2*1}=\frac{4+2\sqrt{258}}{2}
$