3x(x+4)=52

Solution for 3x(x+4)=52 equation:

3x(x+4)=52

We move all terms to the left:

3x(x+4)-(52)=0

We multiply parentheses

3x^2+12x-52=0

a = 3; b = 12; c = -52;
Δ = b2-4ac
Δ = 122-4·3·(-52)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16\sqrt{3}}{2*3}=\frac{-12-16\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16\sqrt{3}}{2*3}=\frac{-12+16\sqrt{3}}{6}
$