x^2-57x+729=0

Solution for x^2-57x+729=0 equation:

x^2-57x+729=0

a = 1; b = -57; c = +729;
Δ = b2-4ac
Δ = -572-4·1·729
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{37}}{2*1}=\frac{57-3\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{37}}{2*1}=\frac{57+3\sqrt{37}}{2}
$