0=5x^2-24x+24

Solution for 0=5x^2-24x+24 equation:

0=5x^2-24x+24

We move all terms to the left:

0-(5x^2-24x+24)=0

We add all the numbers together, and all the variables

-(5x^2-24x+24)=0

We get rid of parentheses

-5x^2+24x-24=0

a = -5; b = 24; c = -24;
Δ = b2-4ac
Δ = 242-4·(-5)·(-24)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{6}}{2*-5}=\frac{-24-4\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{6}}{2*-5}=\frac{-24+4\sqrt{6}}{-10}
$