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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} $
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