x^2-248x+2280=0

Solution for x^2-248x+2280=0 equation:

x^2-248x+2280=0

a = 1; b = -248; c = +2280;
Δ = b2-4ac
Δ = -2482-4·1·2280
Δ = 52384
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:

$\sqrt{\Delta}=\sqrt{52384}=\sqrt{16*3274}=\sqrt{16}*\sqrt{3274}=4\sqrt{3274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-248)-4\sqrt{3274}}{2*1}=\frac{248-4\sqrt{3274}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-248)+4\sqrt{3274}}{2*1}=\frac{248+4\sqrt{3274}}{2}
$