0=33+34x-9x^2

Solution for 0=33+34x-9x^2 equation:

0=33+34x-9x^2

We move all terms to the left:

0-(33+34x-9x^2)=0

We add all the numbers together, and all the variables

-(33+34x-9x^2)=0

We get rid of parentheses

9x^2-34x-33=0

a = 9; b = -34; c = -33;
Δ = b2-4ac
Δ = -342-4·9·(-33)
Δ = 2344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2344}=\sqrt{4*586}=\sqrt{4}*\sqrt{586}=2\sqrt{586}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{586}}{2*9}=\frac{34-2\sqrt{586}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{586}}{2*9}=\frac{34+2\sqrt{586}}{18}
$