4a2-4a-11=0

Solution for 4a2-4a-11=0 equation:

4a^2-4a-11=0

a = 4; b = -4; c = -11;
Δ = b2-4ac
Δ = -42-4·4·(-11)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{3}}{2*4}=\frac{4-8\sqrt{3}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{3}}{2*4}=\frac{4+8\sqrt{3}}{8}
$