48x^2-47x-1=0

Solution for 48x^2-47x-1=0 equation:

48x^2-47x-1=0

a = 48; b = -47; c = -1;
Δ = b2-4ac
Δ = -472-4·48·(-1)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-49}{2*48}=\frac{-2}{96}
=-1/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+49}{2*48}=\frac{96}{96}
=1
$