48x2-13x-1=0

Solution for 48x2-13x-1=0 equation:

48x^2-13x-1=0

a = 48; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·48·(-1)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*48}=\frac{-6}{96}
=-1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*48}=\frac{32}{96}
=1/3
$