X-9+x(6+x)=10+4-(x+7)

Solution for X-9+x(6+x)=10+4-(x+7) equation:

X-9+X(6+X)=10+4-(X+7)

We move all terms to the left:

X-9+X(6+X)-(10+4-(X+7))=0

We add all the numbers together, and all the variables

X+X(X+6)-(10+4-(X+7))-9=0

We multiply parentheses

X^2+X+6X-(10+4-(X+7))-9=0


We calculate terms in parentheses: -(10+4-(X+7)), so:

10+4-(X+7)

determiningTheFunctionDomain
-(X+7)+10+4

We add all the numbers together, and all the variables

-(X+7)+14

We get rid of parentheses

-X-7+14

We add all the numbers together, and all the variables

-1X+7

Back to the equation:

-(-1X+7)


We add all the numbers together, and all the variables

X^2+7X-(-1X+7)-9=0

We get rid of parentheses

X^2+7X+1X-7-9=0

We add all the numbers together, and all the variables

X^2+8X-16=0

a = 1; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·1·(-16)
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{-(8)-8\sqrt{2}}{2*1}=\frac{-8-8\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*1}=\frac{-8+8\sqrt{2}}{2}
$