3x(x+5)=33

Solution for 3x(x+5)=33 equation:

3x(x+5)=33

We move all terms to the left:

3x(x+5)-(33)=0

We multiply parentheses

3x^2+15x-33=0

a = 3; b = 15; c = -33;
Δ = b2-4ac
Δ = 152-4·3·(-33)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{69}}{2*3}=\frac{-15-3\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{69}}{2*3}=\frac{-15+3\sqrt{69}}{6}
$