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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-2x^2+4x+9x-18)=0

We get rid of parentheses

-2x^2+4x+9x-18=0

We add all the numbers together, and all the variables

-2x^2+13x-18=0

a = -2; b = 13; c = -18;
Δ = b2-4ac
Δ = 132-4·(-2)·(-18)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*-2}=\frac{-8}{-4}
=+2
$