2x^2-17x=84

Solution for 2x^2-17x=84 equation:

2x^2-17x=84

We move all terms to the left:

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
$