x^2-46x-480=0

Solution for x^2-46x-480=0 equation:

x^2-46x-480=0

a = 1; b = -46; c = -480;
Δ = b2-4ac
Δ = -462-4·1·(-480)
Δ = 4036
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:

$\sqrt{\Delta}=\sqrt{4036}=\sqrt{4*1009}=\sqrt{4}*\sqrt{1009}=2\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{1009}}{2*1}=\frac{46-2\sqrt{1009}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{1009}}{2*1}=\frac{46+2\sqrt{1009}}{2}
$