x(3x+9)=5670

Solution for x(3x+9)=5670 equation:

x(3x+9)=5670

We move all terms to the left:

x(3x+9)-(5670)=0

We multiply parentheses

3x^2+9x-5670=0

a = 3; b = 9; c = -5670;
Δ = b2-4ac
Δ = 92-4·3·(-5670)
Δ = 68121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{68121}=261$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-261}{2*3}=\frac{-270}{6}
=-45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+261}{2*3}=\frac{252}{6}
=42
$