4(x^2+6x+9)=47

Solution for 4(x^2+6x+9)=47 equation:

4(x^2+6x+9)=47

We move all terms to the left:

4(x^2+6x+9)-(47)=0

We multiply parentheses

4x^2+24x+36-47=0

We add all the numbers together, and all the variables

4x^2+24x-11=0

a = 4; b = 24; c = -11;
Δ = b2-4ac
Δ = 242-4·4·(-11)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{47}}{2*4}=\frac{-24-4\sqrt{47}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{47}}{2*4}=\frac{-24+4\sqrt{47}}{8}
$