Electris Field Quest confuzzled

[9giddjl]

Homework Statement

Two point chagres A= 3.5 x 10^-6 and B= 2.5 x 10^-6 are separated by a distance of 15 cm. Determine the point between the charges at which the electric field strength is zero.

this was an example in the physics textbook i use and this is the answer they came up with


Ea=Eb

Step 1: 9.00 x 10^9 x 3.5 x 10^-6/ s^2 = 9.00 x 10^9 x 2.5 x 10^-6/ (15 - s)^2

Step 2: 3.5 x 10^-6 (15-s)^2= 2.5 x 10^-6 x s^2
Step 3: 0.3s^2 - 30s + 225= 0
s= 8.1 cm from A

I understand it all until Step 3: what have they done there?

 

[Gear300]

They expanded step 2 and set it up so that s could be solved as a root value (its a mathematical step, not much physical analysis).

 

[baba89]

In Step 3, the textbook is using the quadratic formula to solve for the value of s, which represents the distance from point A to the point where the electric field strength is zero. The quadratic formula is used to solve equations in the form of ax^2 + bx + c = 0, where a, b, and c are constants. In this case, the equation is 0.3s^2 - 30s + 225 = 0, with a = 0.3, b = -30, and c = 225. By plugging in these values into the quadratic formula, we can solve for the value of s.