-3k^2+56k+181=0

Solution for -3k^2+56k+181=0 equation:

-3k^2+56k+181=0

a = -3; b = 56; c = +181;
Δ = b2-4ac
Δ = 562-4·(-3)·181
Δ = 5308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5308}=\sqrt{4*1327}=\sqrt{4}*\sqrt{1327}=2\sqrt{1327}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{1327}}{2*-3}=\frac{-56-2\sqrt{1327}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{1327}}{2*-3}=\frac{-56+2\sqrt{1327}}{-6}
$