2+33x-16x^2=18

Solution for 2+33x-16x^2=18 equation:

2+33x-16x^2=18

We move all terms to the left:

2+33x-16x^2-(18)=0

We add all the numbers together, and all the variables

-16x^2+33x-16=0

a = -16; b = 33; c = -16;
Δ = b2-4ac
Δ = 332-4·(-16)·(-16)
Δ = 65
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{-(33)-\sqrt{65}}{2*-16}=\frac{-33-\sqrt{65}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{65}}{2*-16}=\frac{-33+\sqrt{65}}{-32}
$