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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+24x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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