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:
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The automatic solver does not spell it out, but
and  , so it calculates the answers as
 and
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