2x^2-32x-1=0

Solution for 2x^2-32x-1=0 equation:

2x^2-32x-1=0

a = 2; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·2·(-1)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{258}}{2*2}=\frac{32-2\sqrt{258}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{258}}{2*2}=\frac{32+2\sqrt{258}}{4}
$