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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(9+2x(x-2)), so:

9+2x(x-2)

determiningTheFunctionDomain
2x(x-2)+9

We multiply parentheses

2x^2-4x+9

Back to the equation:

-(2x^2-4x+9)


We get rid of parentheses

x^2-2x^2+7x+4x-9-9=0

We add all the numbers together, and all the variables

-1x^2+11x-18=0

a = -1; b = 11; c = -18;
Δ = b2-4ac
Δ = 112-4·(-1)·(-18)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*-1}=\frac{-4}{-2}
=+2
$