-8x2-4x+14=0

Solution for -8x2-4x+14=0 equation:

-8x^2-4x+14=0

a = -8; b = -4; c = +14;
Δ = b2-4ac
Δ = -42-4·(-8)·14
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{29}}{2*-8}=\frac{4-4\sqrt{29}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{29}}{2*-8}=\frac{4+4\sqrt{29}}{-16}
$