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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5u^2+4u+40u-32)=0

We get rid of parentheses

-5u^2+4u+40u-32=0

We add all the numbers together, and all the variables

-5u^2+44u-32=0

a = -5; b = 44; c = -32;
Δ = b2-4ac
Δ = 442-4·(-5)·(-32)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-36}{2*-5}=\frac{-80}{-10}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+36}{2*-5}=\frac{-8}{-10}
=4/5
$