x^2-2x-52=0

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

x^2-2x-52=0

a = 1; b = -2; c = -52;
Δ = b2-4ac
Δ = -22-4·1·(-52)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{53}}{2*1}=\frac{2-2\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{53}}{2*1}=\frac{2+2\sqrt{53}}{2}
$