(X+3)(2x-1)+x+6x+9=0

Solution for (X+3)(2x-1)+x+6x+9=0 equation:

(X+3)(2X-1)+X+6X+9=0

We add all the numbers together, and all the variables

7X+(X+3)(2X-1)+9=0

We multiply parentheses ..

(+2X^2-1X+6X-3)+7X+9=0

We get rid of parentheses

2X^2-1X+6X+7X-3+9=0

We add all the numbers together, and all the variables

2X^2+12X+6=0

a = 2; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·2·6
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*2}=\frac{-12-4\sqrt{6}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*2}=\frac{-12+4\sqrt{6}}{4}
$