2(x+9)(x+3)=19

Solution for 2(x+9)(x+3)=19 equation:

2(x+9)(x+3)=19

We move all terms to the left:

2(x+9)(x+3)-(19)=0

We multiply parentheses ..

2(+x^2+3x+9x+27)-19=0

We multiply parentheses

2x^2+6x+18x+54-19=0

We add all the numbers together, and all the variables

2x^2+24x+35=0

a = 2; b = 24; c = +35;
Δ = b2-4ac
Δ = 242-4·2·35
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{74}}{2*2}=\frac{-24-2\sqrt{74}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{74}}{2*2}=\frac{-24+2\sqrt{74}}{4}
$