-x^2-8x+33=0

Solution for -x^2-8x+33=0 equation:

-x^2-8x+33=0

We add all the numbers together, and all the variables

-1x^2-8x+33=0

a = -1; b = -8; c = +33;
Δ = b2-4ac
Δ = -82-4·(-1)·33
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-14}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+14}{2*-1}=\frac{22}{-2}
=-11
$