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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5u^2+33u+56=0

a = -5; b = 33; c = +56;
Δ = b2-4ac
Δ = 332-4·(-5)·56
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-47}{2*-5}=\frac{-80}{-10}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+47}{2*-5}=\frac{14}{-10}
=-1+2/5
$