0=-2x2-17x+84

Solution for 0=-2x2-17x+84 equation:

0=-2x^2-17x+84

We move all terms to the left:

0-(-2x^2-17x+84)=0

We add all the numbers together, and all the variables

-(-2x^2-17x+84)=0

We get rid of parentheses

2x^2+17x-84=0

a = 2; b = 17; c = -84;
Δ = b2-4ac
Δ = 172-4·2·(-84)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*2}=\frac{14}{4}
=3+1/2
$