8x^2-32x-165=0

Solution for 8x^2-32x-165=0 equation:

8x^2-32x-165=0

a = 8; b = -32; c = -165;
Δ = b2-4ac
Δ = -322-4·8·(-165)
Δ = 6304
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:

$\sqrt{\Delta}=\sqrt{6304}=\sqrt{16*394}=\sqrt{16}*\sqrt{394}=4\sqrt{394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{394}}{2*8}=\frac{32-4\sqrt{394}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{394}}{2*8}=\frac{32+4\sqrt{394}}{16}
$