4x(6x+8)=144

Solution for 4x(6x+8)=144 equation:

4x(6x+8)=144

We move all terms to the left:

4x(6x+8)-(144)=0

We multiply parentheses

24x^2+32x-144=0

a = 24; b = 32; c = -144;
Δ = b2-4ac
Δ = 322-4·24·(-144)
Δ = 14848
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:

$\sqrt{\Delta}=\sqrt{14848}=\sqrt{256*58}=\sqrt{256}*\sqrt{58}=16\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16\sqrt{58}}{2*24}=\frac{-32-16\sqrt{58}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16\sqrt{58}}{2*24}=\frac{-32+16\sqrt{58}}{48}
$