X^2-82x+529=0

Solution for X^2-82x+529=0 equation:

X^2-82X+529=0

a = 1; b = -82; c = +529;
Δ = b2-4ac
Δ = -822-4·1·529
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-48\sqrt{2}}{2*1}=\frac{82-48\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+48\sqrt{2}}{2*1}=\frac{82+48\sqrt{2}}{2}
$