x^2-52x+2=0

Solution for x^2-52x+2=0 equation:

x^2-52x+2=0

a = 1; b = -52; c = +2;
Δ = b2-4ac
Δ = -522-4·1·2
Δ = 2696
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:

$\sqrt{\Delta}=\sqrt{2696}=\sqrt{4*674}=\sqrt{4}*\sqrt{674}=2\sqrt{674}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-2\sqrt{674}}{2*1}=\frac{52-2\sqrt{674}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+2\sqrt{674}}{2*1}=\frac{52+2\sqrt{674}}{2}
$