12x^2-56x-11=0

Solution for 12x^2-56x-11=0 equation:

12x^2-56x-11=0

a = 12; b = -56; c = -11;
Δ = b2-4ac
Δ = -562-4·12·(-11)
Δ = 3664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3664}=\sqrt{16*229}=\sqrt{16}*\sqrt{229}=4\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{229}}{2*12}=\frac{56-4\sqrt{229}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{229}}{2*12}=\frac{56+4\sqrt{229}}{24}
$