(5u-2)(9-u)=0

Solution for (5u-2)(9-u)=0 equation:

(5u-2)(9-u)=0

We add all the numbers together, and all the variables

(5u-2)(-1u+9)=0

We multiply parentheses ..

(-5u^2+45u+2u-18)=0

We get rid of parentheses

-5u^2+45u+2u-18=0

We add all the numbers together, and all the variables

-5u^2+47u-18=0

a = -5; b = 47; c = -18;
Δ = b2-4ac
Δ = 472-4·(-5)·(-18)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-43}{2*-5}=\frac{-90}{-10}
=+9
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+43}{2*-5}=\frac{-4}{-10}
=2/5
$