7+x=42+x(2*7+x)

Solution for 7+x=42+x(2*7+x) equation:

7+x=42+x(2*7+x)

We move all terms to the left:

7+x-(42+x(2*7+x))=0

We add all the numbers together, and all the variables

x-(42+x(x+14))+7=0


We calculate terms in parentheses: -(42+x(x+14)), so:

42+x(x+14)

determiningTheFunctionDomain
x(x+14)+42

We multiply parentheses

x^2+14x+42

Back to the equation:

-(x^2+14x+42)


We get rid of parentheses

-x^2+x-14x-42+7=0

We add all the numbers together, and all the variables

-1x^2-13x-35=0

a = -1; b = -13; c = -35;
Δ = b2-4ac
Δ = -132-4·(-1)·(-35)
Δ = 29
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{-(-13)-\sqrt{29}}{2*-1}=\frac{13-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{29}}{2*-1}=\frac{13+\sqrt{29}}{-2}
$