x^2-64x+225=0

Solution for x^2-64x+225=0 equation:

x^2-64x+225=0

a = 1; b = -64; c = +225;
Δ = b2-4ac
Δ = -642-4·1·225
Δ = 3196
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:

$\sqrt{\Delta}=\sqrt{3196}=\sqrt{4*799}=\sqrt{4}*\sqrt{799}=2\sqrt{799}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{799}}{2*1}=\frac{64-2\sqrt{799}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{799}}{2*1}=\frac{64+2\sqrt{799}}{2}
$