can someone explain to me this please....

What is the difference between

ax^2+bx+c and ax^2+bx+c=0

One is an expression and the other is an equation. (An equation uses an equals sign.)

I hope this helps and is what you were asking.

well you got to equal it e.g:
3x-1=5
3x=5+1( for removing the "-1" you got to add 1 so you gotta do the same on the other side )
3x/3= 5/3( to remove the 3 from 3x as 3x= 3X x so you got to do the same both the side to keep it equal
1x=2
x=2

hope that the answer to your question!!

To clarify, the expression ax^2 + bx + c represents a quadratic function in the form of a polynomial. It is simply an expression that can be simplified or evaluated for a given value of x. For example, you can substitute a numerical value for x and calculate the corresponding output value.

On the other hand, the equation ax^2 + bx + c = 0 is a quadratic equation. The equal sign indicates that the expression on the left side is equal to zero. The purpose of solving a quadratic equation is to find the values of x that make the equation true.

In your example, 3x - 1 = 5 is a linear equation, not a quadratic equation. However, the steps you provided for solving the linear equation are correct. You isolate the variable x by performing the same operation on both sides of the equation to maintain equivalence. Finally, you solve for x by simplifying the expression.

To solve a quadratic equation, you would usually employ techniques such as factoring, completing the square, or using the quadratic formula. These methods are specific to quadratic equations and involve more complex algebraic manipulations.