(X-9)(x-9)=4(x-2)

Solution for (X-9)(x-9)=4(x-2) equation:

(X-9)(X-9)=4(X-2)

We move all terms to the left:

(X-9)(X-9)-(4(X-2))=0

We multiply parentheses ..

(+X^2-9X-9X+81)-(4(X-2))=0


We calculate terms in parentheses: -(4(X-2)), so:

4(X-2)

We multiply parentheses

4X-8

Back to the equation:

-(4X-8)


We get rid of parentheses

X^2-9X-9X-4X+81+8=0

We add all the numbers together, and all the variables

X^2-22X+89=0

a = 1; b = -22; c = +89;
Δ = b2-4ac
Δ = -222-4·1·89
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8\sqrt{2}}{2*1}=\frac{22-8\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8\sqrt{2}}{2*1}=\frac{22+8\sqrt{2}}{2}
$