0=2x^2-22x-204

Solution for 0=2x^2-22x-204 equation:

0=2x^2-22x-204

We move all terms to the left:

0-(2x^2-22x-204)=0

We add all the numbers together, and all the variables

-(2x^2-22x-204)=0

We get rid of parentheses

-2x^2+22x+204=0

a = -2; b = 22; c = +204;
Δ = b2-4ac
Δ = 222-4·(-2)·204
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-46}{2*-2}=\frac{-68}{-4}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+46}{2*-2}=\frac{24}{-4}
=-6
$