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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5u^2+43u+24=0

a = 5; b = 43; c = +24;
Δ = b2-4ac
Δ = 432-4·5·24
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-37}{2*5}=\frac{-80}{10}
=-8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+37}{2*5}=\frac{-6}{10}
=-3/5
$