3x(2x+12)=48

Solution for 3x(2x+12)=48 equation:

3x(2x+12)=48

We move all terms to the left:

3x(2x+12)-(48)=0

We multiply parentheses

6x^2+36x-48=0

a = 6; b = 36; c = -48;
Δ = b2-4ac
Δ = 362-4·6·(-48)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{17}}{2*6}=\frac{-36-12\sqrt{17}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{17}}{2*6}=\frac{-36+12\sqrt{17}}{12}
$