22=-16x^2+33x+6

Solution for 22=-16x^2+33x+6 equation:

22=-16x^2+33x+6

We move all terms to the left:

22-(-16x^2+33x+6)=0

We get rid of parentheses

16x^2-33x-6+22=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}
$