-16x^2+48x+2=0

Solution for -16x^2+48x+2=0 equation:

-16x^2+48x+2=0

a = -16; b = 48; c = +2;
Δ = b2-4ac
Δ = 482-4·(-16)·2
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*-16}=\frac{-48-8\sqrt{38}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{38}}{2*-16}=\frac{-48+8\sqrt{38}}{-32}
$