-x^2+27x-182=0

Solution for -x^2+27x-182=0 equation:

-x^2+27x-182=0

We add all the numbers together, and all the variables

-1x^2+27x-182=0

a = -1; b = 27; c = -182;
Δ = b2-4ac
Δ = 272-4·(-1)·(-182)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-1}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+1}{2*-1}=\frac{-26}{-2}
=+13
$