Question

How do you solve `24x ^ { 2} - 14x = 6`?

Answer 1

`x=(7+sqrt 193)/24, (7-sqrt 193)/24`

Explanation:

Solve `24x^2-14x=6`

Subtract `6` from both sides.

`24x-14x-6=0`

This is a quadratic equation in the form `ax^2+bx+c`, where `a=24`, `b=-14`, and `c=-6`. This equation can be solved using the quadratic formula.

`x=(-b+-sqrt(b^2-4ac))/(2a)`

Substitute the given values into the formula.

`x=(-(-14)+-sqrt(-14^2-4*24*-6))/(2*24)`

`x=(14+-sqrt(196-(-576)))/48`

`x=(14+-sqrt(772))/48`

Prime factorize `sqrt772`.

`x=(14+-sqrt(2xx2xx193))/48`

I used a prime factorization calculator at http://www.calculatorsoup.com/calculators/math/prime-factors.php

`x=(14+-2sqrt 193)/48`

Simplify.

`x=(7+-sqrt 193)/24`

`x=(7+sqrt 193)/24, (7-sqrt 193)/24`