24x^2+16x=144

Solution for 24x^2+16x=144 equation:

24x^2+16x=144

We move all terms to the left:

24x^2+16x-(144)=0

a = 24; b = 16; c = -144;
Δ = b2-4ac
Δ = 162-4·24·(-144)
Δ = 14080
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:

$\sqrt{\Delta}=\sqrt{14080}=\sqrt{256*55}=\sqrt{256}*\sqrt{55}=16\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{55}}{2*24}=\frac{-16-16\sqrt{55}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{55}}{2*24}=\frac{-16+16\sqrt{55}}{48}
$