32x^2-48x-1=0

Solution for 32x^2-48x-1=0 equation:

32x^2-48x-1=0

a = 32; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·32·(-1)
Δ = 2432
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:

$\sqrt{\Delta}=\sqrt{2432}=\sqrt{64*38}=\sqrt{64}*\sqrt{38}=8\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{38}}{2*32}=\frac{48-8\sqrt{38}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{38}}{2*32}=\frac{48+8\sqrt{38}}{64}
$