2x^2=x+6

Solving quadratics by factoring

  x = -3/2 or +2

Step-by-step explanation:

Write in standard form:

  2x^2 -x -6 = 0

Find factors of 2(-6), the product of the first and last coefficients, that have a sum of -1, the middle coefficient.

  -12 = -4·3

Split the middle term using those factors:

  2x^2 -4x +3x -6 = 0

Factor the pairs of terms:

  2x(x -2)+3(x -2) = 0

  (2x +3)(x -2) = 0

Use the zero product rule to identify solutions.

  2x +3 = 0   ⇒   x = -3/2

  x -2 = 0   ⇒   x = 2

y=mx+b

step-by-step explanation:

m slope

b y-intercept

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50