(2u-1)(8-u)=0

Solution for (2u-1)(8-u)=0 equation:

(2u-1)(8-u)=0

We add all the numbers together, and all the variables

(2u-1)(-1u+8)=0

We multiply parentheses ..

(-2u^2+16u+u-8)=0

We get rid of parentheses

-2u^2+16u+u-8=0

We add all the numbers together, and all the variables

-2u^2+17u-8=0

a = -2; b = 17; c = -8;
Δ = b2-4ac
Δ = 172-4·(-2)·(-8)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-15}{2*-2}=\frac{-32}{-4}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+15}{2*-2}=\frac{-2}{-4}
=1/2
$