(2x-9)(-x+3)=0

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

(2x-9)(-x+3)=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2x^2+6x+9x-27)=0

We get rid of parentheses

-2x^2+6x+9x-27=0

We add all the numbers together, and all the variables

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

a = -2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·(-2)·(-27)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*-2}=\frac{-12}{-4}
=+3
$