x^2-78x+716=0

Solution for x^2-78x+716=0 equation:

x^2-78x+716=0

a = 1; b = -78; c = +716;
Δ = b2-4ac
Δ = -782-4·1·716
Δ = 3220
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:

$\sqrt{\Delta}=\sqrt{3220}=\sqrt{4*805}=\sqrt{4}*\sqrt{805}=2\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{805}}{2*1}=\frac{78-2\sqrt{805}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{805}}{2*1}=\frac{78+2\sqrt{805}}{2}
$