(4-u)(5u-8)=0

Solution for (4-u)(5u-8)=0 equation:

(4-u)(5u-8)=0

We add all the numbers together, and all the variables

(-1u+4)(5u-8)=0

We multiply parentheses ..

(-5u^2+8u+20u-32)=0

We get rid of parentheses

-5u^2+8u+20u-32=0

We add all the numbers together, and all the variables

-5u^2+28u-32=0

a = -5; b = 28; c = -32;
Δ = b2-4ac
Δ = 282-4·(-5)·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12}{2*-5}=\frac{-40}{-10}
=+4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12}{2*-5}=\frac{-16}{-10}
=1+3/5
$