4+2x(X+8)=52

Solution for 4+2x(X+8)=52 equation:

4+2x(x+8)=52

We move all terms to the left:

4+2x(x+8)-(52)=0

We add all the numbers together, and all the variables

2x(x+8)-48=0

We multiply parentheses

2x^2+16x-48=0

a = 2; b = 16; c = -48;
Δ = b2-4ac
Δ = 162-4·2·(-48)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{10}}{2*2}=\frac{-16-8\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{10}}{2*2}=\frac{-16+8\sqrt{10}}{4}
$