x(2x+19)=-9

Solution for x(2x+19)=-9 equation:

x(2x+19)=-9

We move all terms to the left:

x(2x+19)-(-9)=0

We add all the numbers together, and all the variables

x(2x+19)+9=0

We multiply parentheses

2x^2+19x+9=0

a = 2; b = 19; c = +9;
Δ = b2-4ac
Δ = 192-4·2·9
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-17}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+17}{2*2}=\frac{-2}{4}
=-1/2
$