2e^2-8e-14=0

Solution for 2e^2-8e-14=0 equation:

2e^2-8e-14=0

a = 2; b = -8; c = -14;
Δ = b2-4ac
Δ = -82-4·2·(-14)
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{11}}{2*2}=\frac{8-4\sqrt{11}}{4}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{11}}{2*2}=\frac{8+4\sqrt{11}}{4}
$