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

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

(2x-9)(x-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{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*2}=\frac{18}{4}
=4+1/2
$