Solve , x^2 / 3(x -7) = -2
First, do the distributive:
3(x -7) = 3 . X + 3 . -7
3(x -7) = 3x - 21
Then,
x^2 / 3(x -7) = -2
x^2 / (3x - 21) = -2
Now, pass the term (3x - 21) to the right side of equation.
x^2 = (3x - 21) . - 2
Use the distributive again
x^2 = 3x .(- 2) -21 . -2
x^2 = -6x + 42
Pass the terms -6x + 42 to the left side of equation. But, changing the sinal
x^2 + 6x - 42 = 0
We have a equation of bhaskara
Where,
a = 1
b = 6
c = -42
Delta = b^2 - 4 . ac
Delta = 6^2 - 4.1.(-42)
Delta = 36 + 168
Delta = 204
Then,
x = [ - b + / - √(Delta) ]/2a
x = [ -6 +/- √(204) ]/2(1)
x = [ -6 +/- √(4×51) ]/2
x = [ - 6 +/- 2√(51) ]/2
Then, we will have two answer
x = [ - 6 - 2√(51)]/2
x = -3 - √(51)
Or
x = [ - 6 + 2√(51) ]/2
x = -3 + √(51)