(x*x-14x+49)/(x*x-49)=3/17

Solution for (x*x-14x+49)/(x*x-49)=3/17 equation:

(x*x-14x+49)/(x*x-49)=3/17

We move all terms to the left:

(x*x-14x+49)/(x*x-49)-(3/17)=0


Domain of the equation: (x*x-49)!=0

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

x*x!=49

x!=49/1

x!=49

x∈R


We add all the numbers together, and all the variables

(-14x+x*x+49)/(x*x-49)-(+3/17)=0

We get rid of parentheses

(-14x+x*x+49)/(x*x-49)-3/17=0

We calculate fractions


(-3x^2+147)/(17x^2-833)+(17x^2-238x+833)/(17x^2-833)=0

We multiply all the terms by the denominator


(-3x^2+147)+(17x^2-238x+833)=0

We get rid of parentheses

-3x^2+17x^2-238x+147+833=0

We add all the numbers together, and all the variables

14x^2-238x+980=0

a = 14; b = -238; c = +980;
Δ = b2-4ac
Δ = -2382-4·14·980
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-238)-42}{2*14}=\frac{196}{28}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-238)+42}{2*14}=\frac{280}{28}
=10
$