(8-u)(3u+5)=0

Solution for (8-u)(3u+5)=0 equation:

(8-u)(3u+5)=0

We add all the numbers together, and all the variables

(-1u+8)(3u+5)=0

We multiply parentheses ..

(-3u^2-5u+24u+40)=0

We get rid of parentheses

-3u^2-5u+24u+40=0

We add all the numbers together, and all the variables

-3u^2+19u+40=0

a = -3; b = 19; c = +40;
Δ = b2-4ac
Δ = 192-4·(-3)·40
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-29}{2*-3}=\frac{-48}{-6}
=+8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+29}{2*-3}=\frac{10}{-6}
=-1+2/3
$