4x2-72=24x

Solution for 4x2-72=24x equation:

4x^2-72=24x

We move all terms to the left:

4x^2-72-(24x)=0

a = 4; b = -24; c = -72;
Δ = b2-4ac
Δ = -242-4·4·(-72)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{3}}{2*4}=\frac{24-24\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{3}}{2*4}=\frac{24+24\sqrt{3}}{8}
$