2x^2-2x-11.5=0

Solution for 2x^2-2x-11.5=0 equation:

2x^2-2x-11.5=0

a = 2; b = -2; c = -11.5;
Δ = b2-4ac
Δ = -22-4·2·(-11.5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{6}}{2*2}=\frac{2-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{6}}{2*2}=\frac{2+4\sqrt{6}}{4}
$