(x-2)-(x-7)(x-9)=0

Solution for (x-2)-(x-7)(x-9)=0 equation:

(x-2)-(x-7)(x-9)=0

We get rid of parentheses

x-(x-7)(x-9)-2=0

We multiply parentheses ..

-(+x^2-9x-7x+63)+x-2=0

We get rid of parentheses

-x^2+9x+7x+x-63-2=0

We add all the numbers together, and all the variables

-1x^2+17x-65=0

a = -1; b = 17; c = -65;
Δ = b2-4ac
Δ = 172-4·(-1)·(-65)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{29}}{2*-1}=\frac{-17-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{29}}{2*-1}=\frac{-17+\sqrt{29}}{-2}
$