3x(x+2)=48

Solution for 3x(x+2)=48 equation:

3x(x+2)=48

We move all terms to the left:

3x(x+2)-(48)=0

We multiply parentheses

3x^2+6x-48=0

a = 3; b = 6; c = -48;
Δ = b2-4ac
Δ = 62-4·3·(-48)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{17}}{2*3}=\frac{-6-6\sqrt{17}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{17}}{2*3}=\frac{-6+6\sqrt{17}}{6}
$