4x(x+8)=52

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

4x(x+8)=52

We move all terms to the left:

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

We multiply parentheses

4x^2+32x-52=0

a = 4; b = 32; c = -52;
Δ = b2-4ac
Δ = 322-4·4·(-52)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{29}}{2*4}=\frac{-32-8\sqrt{29}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{29}}{2*4}=\frac{-32+8\sqrt{29}}{8}
$