(8-u)(5u-7)=0

Solution for (8-u)(5u-7)=0 equation:

(8-u)(5u-7)=0

We add all the numbers together, and all the variables

(-1u+8)(5u-7)=0

We multiply parentheses ..

(-5u^2+7u+40u-56)=0

We get rid of parentheses

-5u^2+7u+40u-56=0

We add all the numbers together, and all the variables

-5u^2+47u-56=0

a = -5; b = 47; c = -56;
Δ = b2-4ac
Δ = 472-4·(-5)·(-56)
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{-(47)-33}{2*-5}=\frac{-80}{-10}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+33}{2*-5}=\frac{-14}{-10}
=1+2/5
$