-2k^2+3K+54=0

Solution for -2k^2+3K+54=0 equation:

-2k^2+3+54=0

We add all the numbers together, and all the variables

-2k^2+57=0

a = -2; b = 0; c = +57;
Δ = b2-4ac
Δ = 02-4·(-2)·57
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{114}}{2*-2}=\frac{0-2\sqrt{114}}{-4}
=-\frac{2\sqrt{114}}{-4}
=-\frac{\sqrt{114}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{114}}{2*-2}=\frac{0+2\sqrt{114}}{-4}
=\frac{2\sqrt{114}}{-4}
=\frac{\sqrt{114}}{-2}
$