2v^2-2v-11=0

Solution for 2v^2-2v-11=0 equation:

2v^2-2v-11=0

a = 2; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·2·(-11)
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{23}}{2*2}=\frac{2-2\sqrt{23}}{4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{23}}{2*2}=\frac{2+2\sqrt{23}}{4}
$