8x(9-x)=24

Solution for 8x(9-x)=24 equation:

8x(9-x)=24

We move all terms to the left:

8x(9-x)-(24)=0

We add all the numbers together, and all the variables

8x(-1x+9)-24=0

We multiply parentheses

-8x^2+72x-24=0

a = -8; b = 72; c = -24;
Δ = b2-4ac
Δ = 722-4·(-8)·(-24)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-8\sqrt{69}}{2*-8}=\frac{-72-8\sqrt{69}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+8\sqrt{69}}{2*-8}=\frac{-72+8\sqrt{69}}{-16}
$