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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+5u^2+25u-8u-40)=0

We get rid of parentheses

5u^2+25u-8u-40=0

We add all the numbers together, and all the variables

5u^2+17u-40=0

a = 5; b = 17; c = -40;
Δ = b2-4ac
Δ = 172-4·5·(-40)
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{-(17)-33}{2*5}=\frac{-50}{10}
=-5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+33}{2*5}=\frac{16}{10}
=1+3/5
$