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

Solution for (8-u)(5u-1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5u^2+u+40u-8)=0

We get rid of parentheses

-5u^2+u+40u-8=0

We add all the numbers together, and all the variables

-5u^2+41u-8=0

a = -5; b = 41; c = -8;
Δ = b2-4ac
Δ = 412-4·(-5)·(-8)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-39}{2*-5}=\frac{-80}{-10}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+39}{2*-5}=\frac{-2}{-10}
=1/5
$