-16x^2+48x+278=0

Solution for -16x^2+48x+278=0 equation:

-16x^2+48x+278=0

a = -16; b = 48; c = +278;
Δ = b2-4ac
Δ = 482-4·(-16)·278
Δ = 20096
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:

$\sqrt{\Delta}=\sqrt{20096}=\sqrt{64*314}=\sqrt{64}*\sqrt{314}=8\sqrt{314}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{314}}{2*-16}=\frac{-48-8\sqrt{314}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{314}}{2*-16}=\frac{-48+8\sqrt{314}}{-32}
$