4(x+4)2x=52

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

4(x+4)2x=52

We move all terms to the left:

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

We multiply parentheses

8x^2+32x-52=0

a = 8; b = 32; c = -52;
Δ = b2-4ac
Δ = 322-4·8·(-52)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{42}}{2*8}=\frac{-32-8\sqrt{42}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{42}}{2*8}=\frac{-32+8\sqrt{42}}{16}
$