Question

Solve the following problem for the roots by using the quadratic formula. 2(6 - x) = x(x + 5)

Answer 1

Solve for x:
2 (6 - x) = x (x + 5)
Expand out terms of the left hand side:
12 - 2 x = x (x + 5)
Expand out terms of the right hand side:
12 - 2 x = x^2 + 5 x
Subtract x^2 + 5 x from both sides:
-x^2 - 7 x + 12 = 0
Multiply both sides by -1:
x^2 + 7 x - 12 = 0
x = (-7 ± sqrt(7^2 - 4 (-12)))/2 = (-7 ± sqrt(49 + 48))/2 = (-7 ± sqrt(97))/2:
Answer:  x = (-7 + sqrt(97))/2 or x = (-7 - sqrt(97))/2