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

Solution for (8-u)(4u+1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-4u^2-1u+32u+8)=0

We get rid of parentheses

-4u^2-1u+32u+8=0

We add all the numbers together, and all the variables

-4u^2+31u+8=0

a = -4; b = 31; c = +8;
Δ = b2-4ac
Δ = 312-4·(-4)·8
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-33}{2*-4}=\frac{-64}{-8}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+33}{2*-4}=\frac{2}{-8}
=-1/4
$