(X-2)(x-9)=-8

Solution for (X-2)(x-9)=-8 equation:

(X-2)(X-9)=-8

We move all terms to the left:

(X-2)(X-9)-(-8)=0

We add all the numbers together, and all the variables

(X-2)(X-9)+8=0

We multiply parentheses ..

(+X^2-9X-2X+18)+8=0

We get rid of parentheses

X^2-9X-2X+18+8=0

We add all the numbers together, and all the variables

X^2-11X+26=0

a = 1; b = -11; c = +26;
Δ = b2-4ac
Δ = -112-4·1·26
Δ = 17
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{-(-11)-\sqrt{17}}{2*1}=\frac{11-\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{17}}{2*1}=\frac{11+\sqrt{17}}{2}
$