(a^2)-2a-67=0

Solution for (a^2)-2a-67=0 equation:

(a^2)-2a-67=0

a = 1; b = -2; c = -67;
Δ = b2-4ac
Δ = -22-4·1·(-67)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{17}}{2*1}=\frac{2-4\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{17}}{2*1}=\frac{2+4\sqrt{17}}{2}
$