x^2-60x+784=0

Solution for x^2-60x+784=0 equation:

x^2-60x+784=0

a = 1; b = -60; c = +784;
Δ = b2-4ac
Δ = -602-4·1·784
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{29}}{2*1}=\frac{60-4\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{29}}{2*1}=\frac{60+4\sqrt{29}}{2}
$