X^2-60x+640=0

Solution for X^2-60x+640=0 equation:

X^2-60X+640=0

a = 1; b = -60; c = +640;
Δ = b2-4ac
Δ = -602-4·1·640
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{65}}{2*1}=\frac{60-4\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{65}}{2*1}=\frac{60+4\sqrt{65}}{2}
$