(2u-3)(9-u)=0

Solution for (2u-3)(9-u)=0 equation:

(2u-3)(9-u)=0

We add all the numbers together, and all the variables

(2u-3)(-1u+9)=0

We multiply parentheses ..

(-2u^2+18u+3u-27)=0

We get rid of parentheses

-2u^2+18u+3u-27=0

We add all the numbers together, and all the variables

-2u^2+21u-27=0

a = -2; b = 21; c = -27;
Δ = b2-4ac
Δ = 212-4·(-2)·(-27)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-15}{2*-2}=\frac{-36}{-4}
=+9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+15}{2*-2}=\frac{-6}{-4}
=1+1/2
$