-8x^2-27x+14=0

Solution for -8x^2-27x+14=0 equation:

-8x^2-27x+14=0

a = -8; b = -27; c = +14;
Δ = b2-4ac
Δ = -272-4·(-8)·14
Δ = 1177
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{-(-27)-\sqrt{1177}}{2*-8}=\frac{27-\sqrt{1177}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1177}}{2*-8}=\frac{27+\sqrt{1177}}{-16}
$