(5u-9)(3-u)=0

Solution for (5u-9)(3-u)=0 equation:

(5u-9)(3-u)=0

We add all the numbers together, and all the variables

(5u-9)(-1u+3)=0

We multiply parentheses ..

(-5u^2+15u+9u-27)=0

We get rid of parentheses

-5u^2+15u+9u-27=0

We add all the numbers together, and all the variables

-5u^2+24u-27=0

a = -5; b = 24; c = -27;
Δ = b2-4ac
Δ = 242-4·(-5)·(-27)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6}{2*-5}=\frac{-30}{-10}
=+3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6}{2*-5}=\frac{-18}{-10}
=1+4/5
$