0=2x^2+17x-84

Solution for 0=2x^2+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{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+31}{2*-2}=\frac{48}{-4}
=-12
$