8x^2-32x-140=0

Solution for 8x^2-32x-140=0 equation:

8x^2-32x-140=0

a = 8; b = -32; c = -140;
Δ = b2-4ac
Δ = -322-4·8·(-140)
Δ = 5504
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:

$\sqrt{\Delta}=\sqrt{5504}=\sqrt{64*86}=\sqrt{64}*\sqrt{86}=8\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{86}}{2*8}=\frac{32-8\sqrt{86}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{86}}{2*8}=\frac{32+8\sqrt{86}}{16}
$