(x^2+2x+1)/(x^2+6x+9)=36/49

Solution for (x^2+2x+1)/(x^2+6x+9)=36/49 equation:

(x^2+2x+1)/(x^2+6x+9)=36/49

We move all terms to the left:

(x^2+2x+1)/(x^2+6x+9)-(36/49)=0


Domain of the equation: (x^2+6x+9)!=0

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

x^2+6x!=-9

x∈R


We add all the numbers together, and all the variables

(x^2+2x+1)/(x^2+6x+9)-(+36/49)=0

We get rid of parentheses

(x^2+2x+1)/(x^2+6x+9)-36/49=0

We calculate fractions


(-36x^2-216x-324)/(49x^2+294x+441)+(49x^2+98x+49)/(49x^2+294x+441)=0

We multiply all the terms by the denominator


(-36x^2-216x-324)+(49x^2+98x+49)=0

We get rid of parentheses

-36x^2+49x^2-216x+98x-324+49=0

We add all the numbers together, and all the variables

13x^2-118x-275=0

a = 13; b = -118; c = -275;
Δ = b2-4ac
Δ = -1182-4·13·(-275)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-168}{2*13}=\frac{-50}{26}
=-1+12/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+168}{2*13}=\frac{286}{26}
=11
$