3x(x+8)=48

Solution for 3x(x+8)=48 equation:

3x(x+8)=48

We move all terms to the left:

3x(x+8)-(48)=0

We multiply parentheses

3x^2+24x-48=0

a = 3; b = 24; c = -48;
Δ = b2-4ac
Δ = 242-4·3·(-48)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{2}}{2*3}=\frac{-24-24\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{2}}{2*3}=\frac{-24+24\sqrt{2}}{6}
$