-33=3x(x-9)

Solution for -33=3x(x-9) equation:

-33=3x(x-9)

We move all terms to the left:

-33-(3x(x-9))=0


We calculate terms in parentheses: -(3x(x-9)), so:

3x(x-9)

We multiply parentheses

3x^2-27x

Back to the equation:

-(3x^2-27x)


We get rid of parentheses

-3x^2+27x-33=0

a = -3; b = 27; c = -33;
Δ = b2-4ac
Δ = 272-4·(-3)·(-33)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{37}}{2*-3}=\frac{-27-3\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{37}}{2*-3}=\frac{-27+3\sqrt{37}}{-6}
$