3x(4x+2)=144

Solution for 3x(4x+2)=144 equation:

3x(4x+2)=144

We move all terms to the left:

3x(4x+2)-(144)=0

We multiply parentheses

12x^2+6x-144=0

a = 12; b = 6; c = -144;
Δ = b2-4ac
Δ = 62-4·12·(-144)
Δ = 6948
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:

$\sqrt{\Delta}=\sqrt{6948}=\sqrt{36*193}=\sqrt{36}*\sqrt{193}=6\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{193}}{2*12}=\frac{-6-6\sqrt{193}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{193}}{2*12}=\frac{-6+6\sqrt{193}}{24}
$