2x(x+9)=-12

Solution for 2x(x+9)=-12 equation:

2x(x+9)=-12

We move all terms to the left:

2x(x+9)-(-12)=0

We add all the numbers together, and all the variables

2x(x+9)+12=0

We multiply parentheses

2x^2+18x+12=0

a = 2; b = 18; c = +12;
Δ = b2-4ac
Δ = 182-4·2·12
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{57}}{2*2}=\frac{-18-2\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{57}}{2*2}=\frac{-18+2\sqrt{57}}{4}
$