x^2-82x+1456=0

Solution for x^2-82x+1456=0 equation:

x^2-82x+1456=0

a = 1; b = -82; c = +1456;
Δ = b2-4ac
Δ = -822-4·1·1456
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-30}{2*1}=\frac{52}{2}
=26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+30}{2*1}=\frac{112}{2}
=56
$