x^2-129x+4=0

Solution for x^2-129x+4=0 equation:

x^2-129x+4=0

a = 1; b = -129; c = +4;
Δ = b2-4ac
Δ = -1292-4·1·4
Δ = 16625
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:

$\sqrt{\Delta}=\sqrt{16625}=\sqrt{25*665}=\sqrt{25}*\sqrt{665}=5\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-129)-5\sqrt{665}}{2*1}=\frac{129-5\sqrt{665}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+5\sqrt{665}}{2*1}=\frac{129+5\sqrt{665}}{2}
$