3x(2x+1)=33

Solution for 3x(2x+1)=33 equation:

3x(2x+1)=33

We move all terms to the left:

3x(2x+1)-(33)=0

We multiply parentheses

6x^2+3x-33=0

a = 6; b = 3; c = -33;
Δ = b2-4ac
Δ = 32-4·6·(-33)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{89}}{2*6}=\frac{-3-3\sqrt{89}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{89}}{2*6}=\frac{-3+3\sqrt{89}}{12}
$