(5u-9)(4-u)=0

Solution for (5u-9)(4-u)=0 equation:

(5u-9)(4-u)=0

We add all the numbers together, and all the variables

(5u-9)(-1u+4)=0

We multiply parentheses ..

(-5u^2+20u+9u-36)=0

We get rid of parentheses

-5u^2+20u+9u-36=0

We add all the numbers together, and all the variables

-5u^2+29u-36=0

a = -5; b = 29; c = -36;
Δ = b2-4ac
Δ = 292-4·(-5)·(-36)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-11}{2*-5}=\frac{-40}{-10}
=+4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+11}{2*-5}=\frac{-18}{-10}
=1+4/5
$