-16x^2+48x+6=0

Solution for -16x^2+48x+6=0 equation:

-16x^2+48x+6=0

a = -16; b = 48; c = +6;
Δ = b2-4ac
Δ = 482-4·(-16)·6
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{42}}{2*-16}=\frac{-48-8\sqrt{42}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{42}}{2*-16}=\frac{-48+8\sqrt{42}}{-32}
$