Question

Solve for d. (d-e)/(3d +e)=d

Answer 1

`(d-e)/(3d+e)=d\ \ \ \ |\text{cross multiply}\\\\d(3d+e)=d-e\\\\3d^2+de=d-e\ \ \ |-d+e\\\\3d^2+de-d+e=0\\\\3d^2+(e-1)d+e=0`

Use the quadratic formula:

`a=3,\ b=e-1,\ c=e\\\\b^2=(e-1)^2-4(3)(e)=(e-1)^2-12e\\\\d=(-b\pm√(b^2-4ac))/(2a)\\\\d=(-(e-1)\pm√((e-1)^2-12e))/(2\cdot3)\\\\\boxed{d=(1-e\pm√((e-1)^2-12e))/(6)}`