(5u-8)(9+u)=0

Solution for (5u-8)(9+u)=0 equation:

(5u-8)(9+u)=0

We add all the numbers together, and all the variables

(5u-8)(u+9)=0

We multiply parentheses ..

(+5u^2+45u-8u-72)=0

We get rid of parentheses

5u^2+45u-8u-72=0

We add all the numbers together, and all the variables

5u^2+37u-72=0

a = 5; b = 37; c = -72;
Δ = b2-4ac
Δ = 372-4·5·(-72)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-53}{2*5}=\frac{-90}{10}
=-9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+53}{2*5}=\frac{16}{10}
=1+3/5
$