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

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

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

We add all the numbers together, and all the variables

(5u-9)(-1u+5)=0

We multiply parentheses ..

(-5u^2+25u+9u-45)=0

We get rid of parentheses

-5u^2+25u+9u-45=0

We add all the numbers together, and all the variables

-5u^2+34u-45=0

a = -5; b = 34; c = -45;
Δ = b2-4ac
Δ = 342-4·(-5)·(-45)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-16}{2*-5}=\frac{-50}{-10}
=+5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+16}{2*-5}=\frac{-18}{-10}
=1+4/5
$