-x^2+30x-54=0

Solution for -x^2+30x-54=0 equation:

-x^2+30x-54=0

We add all the numbers together, and all the variables

-1x^2+30x-54=0

a = -1; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·(-1)·(-54)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{19}}{2*-1}=\frac{-30-6\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{19}}{2*-1}=\frac{-30+6\sqrt{19}}{-2}
$