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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2-7x-2x+14)-9=0

We get rid of parentheses

x^2-7x-2x+14-9=0

We add all the numbers together, and all the variables

x^2-9x+5=0

a = 1; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·1·5
Δ = 61
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{-(-9)-\sqrt{61}}{2*1}=\frac{9-\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{61}}{2*1}=\frac{9+\sqrt{61}}{2}
$