3x(x+3)=171

Solution for 3x(x+3)=171 equation:

3x(x+3)=171

We move all terms to the left:

3x(x+3)-(171)=0

We multiply parentheses

3x^2+9x-171=0

a = 3; b = 9; c = -171;
Δ = b2-4ac
Δ = 92-4·3·(-171)
Δ = 2133
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:

$\sqrt{\Delta}=\sqrt{2133}=\sqrt{9*237}=\sqrt{9}*\sqrt{237}=3\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{237}}{2*3}=\frac{-9-3\sqrt{237}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{237}}{2*3}=\frac{-9+3\sqrt{237}}{6}
$