(7x+14)/(x+2)=x+2

Solution for (7x+14)/(x+2)=x+2 equation:

(7x+14)/(x+2)=x+2

We move all terms to the left:

(7x+14)/(x+2)-(x+2)=0


Domain of the equation: (x+2)!=0

We move all terms containing x to the left, all other terms to the right

x!=-2

x∈R


We get rid of parentheses

(7x+14)/(x+2)-x-2=0

We multiply all the terms by the denominator


(7x+14)-x*(x+2)-2*(x+2)=0

We multiply parentheses

-x^2+(7x+14)-2x-2x-4=0

We get rid of parentheses

-x^2+7x-2x-2x+14-4=0

We add all the numbers together, and all the variables

-1x^2+3x+10=0

a = -1; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-1)·10
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{-(3)-7}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*-1}=\frac{4}{-2}
=-2
$