a^2-18a-316=0

Solution for a^2-18a-316=0 equation:

a^2-18a-316=0

a = 1; b = -18; c = -316;
Δ = b2-4ac
Δ = -182-4·1·(-316)
Δ = 1588
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:

$\sqrt{\Delta}=\sqrt{1588}=\sqrt{4*397}=\sqrt{4}*\sqrt{397}=2\sqrt{397}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{397}}{2*1}=\frac{18-2\sqrt{397}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{397}}{2*1}=\frac{18+2\sqrt{397}}{2}
$