a^2-36a-1=0

Solution for a^2-36a-1=0 equation:

a^2-36a-1=0

a = 1; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·1·(-1)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-10\sqrt{13}}{2*1}=\frac{36-10\sqrt{13}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+10\sqrt{13}}{2*1}=\frac{36+10\sqrt{13}}{2}
$