x^2-52x-260=0

Solution for x^2-52x-260=0 equation:

x^2-52x-260=0

a = 1; b = -52; c = -260;
Δ = b2-4ac
Δ = -522-4·1·(-260)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-12\sqrt{26}}{2*1}=\frac{52-12\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+12\sqrt{26}}{2*1}=\frac{52+12\sqrt{26}}{2}
$