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

Solution for (3u-1)(8-u)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3u^2+24u+u-8)=0

We get rid of parentheses

-3u^2+24u+u-8=0

We add all the numbers together, and all the variables

-3u^2+25u-8=0

a = -3; b = 25; c = -8;
Δ = b2-4ac
Δ = 252-4·(-3)·(-8)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-23}{2*-3}=\frac{-48}{-6}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+23}{2*-3}=\frac{-2}{-6}
=1/3
$