2x(3+x)+11=29-6

Solution for 2x(3+x)+11=29-6 equation:

2x(3+x)+11=29-6

We move all terms to the left:

2x(3+x)+11-(29-6)=0

We add all the numbers together, and all the variables

2x(x+3)+11-23=0

We add all the numbers together, and all the variables

2x(x+3)-12=0

We multiply parentheses

2x^2+6x-12=0

a = 2; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·2·(-12)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*2}=\frac{-6-2\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*2}=\frac{-6+2\sqrt{33}}{4}
$