a^2-16a-52=0

Solution for a^2-16a-52=0 equation:

a^2-16a-52=0

a = 1; b = -16; c = -52;
Δ = b2-4ac
Δ = -162-4·1·(-52)
Δ = 464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{29}}{2*1}=\frac{16-4\sqrt{29}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{29}}{2*1}=\frac{16+4\sqrt{29}}{2}
$