18=2x^2-3x-17

Solution for 18=2x^2-3x-17 equation:

18=2x^2-3x-17

We move all terms to the left:

18-(2x^2-3x-17)=0

We get rid of parentheses

-2x^2+3x+17+18=0

We add all the numbers together, and all the variables

-2x^2+3x+35=0

a = -2; b = 3; c = +35;
Δ = b2-4ac
Δ = 32-4·(-2)·35
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*-2}=\frac{14}{-4}
=-3+1/2
$