9(x^2+2x+6)=406

Solution for 9(x^2+2x+6)=406 equation:

9(x^2+2x+6)=406

We move all terms to the left:

9(x^2+2x+6)-(406)=0

We multiply parentheses

9x^2+18x+54-406=0

We add all the numbers together, and all the variables

9x^2+18x-352=0

a = 9; b = 18; c = -352;
Δ = b2-4ac
Δ = 182-4·9·(-352)
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-114}{2*9}=\frac{-132}{18}
=-7+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+114}{2*9}=\frac{96}{18}
=5+1/3
$