0=2x2+26x-204

Solution for 0=2x2+26x-204 equation:

0=2x^2+26x-204

We move all terms to the left:

0-(2x^2+26x-204)=0

We add all the numbers together, and all the variables

-(2x^2+26x-204)=0

We get rid of parentheses

-2x^2-26x+204=0

a = -2; b = -26; c = +204;
Δ = b2-4ac
Δ = -262-4·(-2)·204
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{577}}{2*-2}=\frac{26-2\sqrt{577}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{577}}{2*-2}=\frac{26+2\sqrt{577}}{-4}
$