(3u-8)(9-u)=0

Solution for (3u-8)(9-u)=0 equation:

(3u-8)(9-u)=0

We add all the numbers together, and all the variables

(3u-8)(-1u+9)=0

We multiply parentheses ..

(-3u^2+27u+8u-72)=0

We get rid of parentheses

-3u^2+27u+8u-72=0

We add all the numbers together, and all the variables

-3u^2+35u-72=0

a = -3; b = 35; c = -72;
Δ = b2-4ac
Δ = 352-4·(-3)·(-72)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-19}{2*-3}=\frac{-54}{-6}
=+9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+19}{2*-3}=\frac{-16}{-6}
=2+2/3
$