Using the Quadratic Formula to Solve 5x = 6x2 – 3, What Are the Values of X?


Question: Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

The quadratic formula is the easiest way of solving quadratic equations especially when it is difficult to solve by the splitting of the middle term.

Answer: x = [ 5 ± √97 ] / 2  are the solutions of the quadratic equation 5x = 6x2 – 3

Let us use the quadratic formula to solve 5x = 6x2 – 3

Explanation:

Let's write the equation in it's standard form.

5x = 6x2 – 3

6x2 - 5x - 3 = 0

a = 6, b = -5, c = -3          ------->   when we compare with the standard form of a quadratic expression ax2 + bx + c = 0

By quadratic formula,

x = [ -b ± √(b2 - 4ac) ] / 2a

x =  [ -(-5) ± √{(-5)2 - 4(6)(-3)} ] / 2(1)

x =  [ 5 ± √{25 + 72} ] / 2 

x =  [ 5 ± √97 ] / 2 

values of x are:  [ 5 + √97] / 2 and  [ 5 - √97 ] / 2

Both the values of x are irrational numbers.

Thus, we have seen the solutions of the quadratic expression x2 = 5 – x.