Question

Quadratic formula: 3 x ^2 + 45 = 24x

Answer 1

x = 3 or x = 5

Explanation:

The quadratic formula tells the solutions to a quadratic equation based on its coefficients when written in standard form.

Quadratic formula

The solution to ax² +bx +c = 0 is given by ...

`x=(-b\pm√(b^2-4ac))/(2a)`

Application

In order to make use of the formula, we need to find the coefficients when the equation is written in standard form. Subtracting 24x from both sides will put it in that form. We can also save a little bit of work by dividing the resulting equation by the common factor of 3.

3x² -24x +45 = 0 . . . . . . . . subtract 24x

x² -8x +15 = 0 . . . . . . . . . . divide by 3

This leaves us a standard-form equation with a=1, b=-8, c=15. The formula gives the solutions as ...

`x=(-(-8)\pm√((-8)^2-4(1)(15)))/(2(1))=(8\pm√(64 -60))/(2)\\\\x=(8\pm√(4))/(2)=4\pm1\\\\ \boxed{x= \{3, 5\}}`

The solutions to the given quadratic equation are x=3 and x=5.