X-9+x(6+x)=x+4-(x+7)

Solution for X-9+x(6+x)=x+4-(x+7) equation:

X-9+X(6+X)=X+4-(X+7)

We move all terms to the left:

X-9+X(6+X)-(X+4-(X+7))=0

We add all the numbers together, and all the variables

X+X(X+6)-(X+4-(X+7))-9=0

We multiply parentheses

X^2+X+6X-(X+4-(X+7))-9=0


We calculate terms in parentheses: -(X+4-(X+7)), so:

X+4-(X+7)

determiningTheFunctionDomain
X-(X+7)+4

We get rid of parentheses

X-X-7+4

We add all the numbers together, and all the variables

-3

Back to the equation:

-(-3)


We add all the numbers together, and all the variables

X^2+7X-6=0

a = 1; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·1·(-6)
Δ = 73
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{-(7)-\sqrt{73}}{2*1}=\frac{-7-\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*1}=\frac{-7+\sqrt{73}}{2}
$