4x^2-32x^-1=0

Solution for 4x^2-32x^-1=0 equation:

4x^2-32x^-1=0

We add all the numbers together, and all the variables

4x^2-32x-1=0

a = 4; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·4·(-1)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{65}}{2*4}=\frac{32-4\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{65}}{2*4}=\frac{32+4\sqrt{65}}{8}
$