0=2x^2-3x-209

Solution for 0=2x^2-3x-209 equation:

0=2x^2-3x-209

We move all terms to the left:

0-(2x^2-3x-209)=0

We add all the numbers together, and all the variables

-(2x^2-3x-209)=0

We get rid of parentheses

-2x^2+3x+209=0

a = -2; b = 3; c = +209;
Δ = b2-4ac
Δ = 32-4·(-2)·209
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-41}{2*-2}=\frac{-44}{-4}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+41}{2*-2}=\frac{38}{-4}
=-9+1/2
$