a2-8a-11=0

Solution for a2-8a-11=0 equation:

a2-8a-11=0

We add all the numbers together, and all the variables

a^2-8a-11=0

a = 1; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·1·(-11)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{3}}{2*1}=\frac{8-6\sqrt{3}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{3}}{2*1}=\frac{8+6\sqrt{3}}{2}
$