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

We get rid of parentheses

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}
$