-6x^2+48x+200=0

Solution for -6x^2+48x+200=0 equation:

-6x^2+48x+200=0

a = -6; b = 48; c = +200;
Δ = b2-4ac
Δ = 482-4·(-6)·200
Δ = 7104
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:

$\sqrt{\Delta}=\sqrt{7104}=\sqrt{64*111}=\sqrt{64}*\sqrt{111}=8\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{111}}{2*-6}=\frac{-48-8\sqrt{111}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{111}}{2*-6}=\frac{-48+8\sqrt{111}}{-12}
$