h^2-74h+823=0

Solution for h^2-74h+823=0 equation:

h^2-74h+823=0

a = 1; b = -74; c = +823;
Δ = b2-4ac
Δ = -742-4·1·823
Δ = 2184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{546}}{2*1}=\frac{74-2\sqrt{546}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{546}}{2*1}=\frac{74+2\sqrt{546}}{2}
$