-x^2+27x-126=0

Solution for -x^2+27x-126=0 equation:

-x^2+27x-126=0

We add all the numbers together, and all the variables

-1x^2+27x-126=0

a = -1; b = 27; c = -126;
Δ = b2-4ac
Δ = 272-4·(-1)·(-126)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-15}{2*-1}=\frac{-42}{-2}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+15}{2*-1}=\frac{-12}{-2}
=+6
$