2x^2-1.414213562x-2=0

Solution for 2x^2-1.414213562x-2=0 equation:

2x^2-1.414213562x-2=0

a = 2; b = -1.414213562; c = -2;
Δ = b2-4ac
Δ = -1.4142135622-4·2·(-2)
Δ = 17.999999998945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.414213562)-\sqrt{17.999999998945}}{2*2}=\frac{1.414213562-\sqrt{17.999999998945}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.414213562)+\sqrt{17.999999998945}}{2*2}=\frac{1.414213562+\sqrt{17.999999998945}}{4}
$