x^2-112x+780=0

Solution for x^2-112x+780=0 equation:

x^2-112x+780=0

a = 1; b = -112; c = +780;
Δ = b2-4ac
Δ = -1122-4·1·780
Δ = 9424
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:

$\sqrt{\Delta}=\sqrt{9424}=\sqrt{16*589}=\sqrt{16}*\sqrt{589}=4\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{589}}{2*1}=\frac{112-4\sqrt{589}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{589}}{2*1}=\frac{112+4\sqrt{589}}{2}
$