can you explain and answer this equation
8x^2-13x+3=0
To solve the quadratic equation 8x^2 - 13x + 3 = 0, we can use the quadratic formula:
x = (-(-13) ± √((-13)^2 - 4*8*3))/(2*8)
x = (13 ± √(169 - 96))/16
x = (13 ± √73)/16
Therefore, the solutions to the equation are:
x = (13 + √73)/16
x = (13 - √73)/16
can you explain the quadratic formula
The quadratic formula is used to find the solutions of a quadratic equation in the form of ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. The formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this formula:
- "x" represents the variable that we are solving for.
- "a" is the coefficient of the x^2 term.
- "b" is the coefficient of the x term.
- "c" is the constant term.
- The symbol "±" means that there are two possible solutions: one with a plus sign and one with a minus sign.
To use the quadratic formula, plug in the values of a, b, and c from the given quadratic equation into the formula, then simplify to find the solutions for x. Remember that you may have two real solutions, one real solution, or two complex solutions depending on the value inside the square root (the discriminant: b^2 - 4ac).