SOLUTION: Can you please help me solve this equation using quadratic formula? 0.25x^2-0.25x-10.5=0

Question 878201: Can you please help me solve this equation using quadratic formula?
0.25x^2-0.25x-10.5=0
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

The quadratic formula says that the solutions (if any) to an equation of the form
are given by

However, I see no need to make work harder.
The coefficients of
are ugly decimals, and they will make calculations complicated.
A much better looking equivalent equation can be obtained by multiplying both sides of the equal sign times 4:
<-->}<--><-->
is easier to solve by applying the quadratic formula.
(It is also easier to solve by factoring, and by "completing the square").
The equation (usually written as
has , , and .
Applying the quadratic formula we get

That means the solutions are

NOTE:
Of course, you can always apply the quadratic formula to the original equation.
That is easy enough if you have someone else (or something else) do the calculations for you
I that case, you would use , , and
Then invoking the program available here,

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=10.5625 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -6. Here's your graph:

The automatic solver does not spell it out, but

and , so it calculates the answers as
and

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