```Question 597910
Depending on how much you've learned of algebra so far, this could be a little confusing or very confusing, but here it goes.

THE SYMBOLS FOR MULTIPLICATION:
At the bottom of the formula, between the 2 and the a , there is symbol called a middle dot.
That is a symbol used in algebra to mean multiplied by. The expression {{{2*a}}} means 2 times a.
In algebra, the letter x is used a lot. The old X multiplication sign that is used in third grade looks too much like the letter x. That old X symbol could cause confusion, so it is not used.
Sometimes a middle dot is used to indicate multiplication, as in
{{{3*5=15}}} or {{{2*a}}}.
If there is no room for confusion, the middle dot can be skipped, so we are allowed to write {{{2a}}} instead of {{{2*a}}}.
To make matters a little more confusing, the asterisk is used as a middle dot when typing a middle dot symbol is difficult or impossible. So you may see 2*a instead of {{{2a}}} or {{{2*a}}}.

The quadratic formula is used to find solutions to quadratic equations like
{{{15x^2-14x-8=0}}}.
All quadratic equations can be represented with the general equation
{{{ax^2+bx+c=0}}} where a, b, and c represent the numbers in the equation.
For {{{15x^2-14x-8=0}}}, a is 15, b is -14, and c is -8.

Some quadratic equations have one or two real solutions. For other quadratic equations, there is no real number that could be a solution. It all depends on the value of an expression called the discriminant. In the formula you are asking about, the letter d represents the discriminant.

The discriminant is the expression
{{{b^2-4ac}}} The 4, a, and c are multiplied together.
For {{{15x^2-14x-8=0}}}, the discriminant is
{{{(-14)^2-4*15*(-8)=196+480=676}}}

If the discriminant is positive (as for the equation {{{15x^2-14x-8=0}}}, with {{{d=676}}} for a discriminant), there are two distinct (meaning different) real solutions. They can be calculated using the formula
{{{x=(-b +- sqrt(d))/2a}}}
For {{{15x^2-14x-8=0}}}, it would be
{{{x=(-(-14) +- sqrt(676))/(2*15)=(14 +- 26)/30}}}
One solution is
{{{x=(14 + 26)/30=40/30=4/3}}}.
The other is
{{{x=(14 - 26)/30=-12/30=-2/5}}}.```