p^2-10p-52=0

Solution for p^2-10p-52=0 equation:

p^2-10p-52=0

a = 1; b = -10; c = -52;
Δ = b2-4ac
Δ = -102-4·1·(-52)
Δ = 308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{77}}{2*1}=\frac{10-2\sqrt{77}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{77}}{2*1}=\frac{10+2\sqrt{77}}{2}
$