(8-u)(5u+6)=0

Solution for (8-u)(5u+6)=0 equation:

(8-u)(5u+6)=0

We add all the numbers together, and all the variables

(-1u+8)(5u+6)=0

We multiply parentheses ..

(-5u^2-6u+40u+48)=0

We get rid of parentheses

-5u^2-6u+40u+48=0

We add all the numbers together, and all the variables

-5u^2+34u+48=0

a = -5; b = 34; c = +48;
Δ = b2-4ac
Δ = 342-4·(-5)·48
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-46}{2*-5}=\frac{-80}{-10}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+46}{2*-5}=\frac{12}{-10}
=-1+1/5
$