2x^2-3x-2=20589

Solution for 2x^2-3x-2=20589 equation:

2x^2-3x-2=20589

We move all terms to the left:

2x^2-3x-2-(20589)=0

We add all the numbers together, and all the variables

2x^2-3x-20591=0

a = 2; b = -3; c = -20591;
Δ = b2-4ac
Δ = -32-4·2·(-20591)
Δ = 164737
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{164737}}{2*2}=\frac{3-\sqrt{164737}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{164737}}{2*2}=\frac{3+\sqrt{164737}}{4}
$