Question

6x^2-10x-16=0?

Answer 1

Solve the quadratic to get `x=-1, 8/3`

Explanation:

I assume the question wants the solutions for `x`.

Divide through to make the first coefficient 1:
`x^2-5/3x-8/3=0`

Complete the square:
`(x-5/6)^2-25/36-8/3=0`
`(x-5/6)^2=121/36`

`x=5/6+-sqrt(121/36)=5/6+-11/6`

So `x=-1, 8/3`.

Answer 2

`y = 6x^2 - 10x - 16 = 0`
Since a - b + c = 0, use shortcut.
The 2 real roots are:
x = -1 ,and `x = -c/a = 16/6 = 8/3`

Reminder of shortcut .
If a + b + c = 0, the 2 real roots are: x = 1, and `x = c/a`
Example 1. Solve: `3x^2 + 7x - 10 = 0`
x = 1, and `x = c/a = -10/3`
If a - b + c = 0, the 2 real roots are: x = -1, and `x = -c/a`
Example 2. Solve: `4x^2 - 5x - 9 = 0`
x = -1, and `x = -c/a = 9/4`

Answer 3

Another way

Explanation:

if `ax^2+bx+c=0`

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

In this case `a = 6,b=-10, c = -16`

`x = ( -(-10) pm sqrt( (-10)^2 - ( 4 * 6 * (-16 ) ) ) )/(2*6)`

`x = (10pmsqrt(484) )/12`

`x = (10 pm22 )/12`

`x = {8/3 , -1 }`