8x^2-4x-117=0

Solution for 8x^2-4x-117=0 equation:

8x^2-4x-117=0

a = 8; b = -4; c = -117;
Δ = b2-4ac
Δ = -42-4·8·(-117)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{235}}{2*8}=\frac{4-4\sqrt{235}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{235}}{2*8}=\frac{4+4\sqrt{235}}{16}
$