Which of the following is a solution of 4x2 = − 9x − 4?

The solutions are:

x1 = (- 9 + √17)/8 = -0.6

x2 = (-9 -  √17)/8 = -1.6

Step-by-step explanation:

We have the equation:

4*x^2 = -9x - 4

first we put all the terms in one side of the equation:

4x^2 + 9x + 4 = 0

now, we use the Bhaskara's equation to find the roots:

where for a function:

ax^2 + bx + c = 0

the roots are:

x = (-b +- √(b^2 - 4ac))/2a

where each root takes one of the possible signs of the square root.

so, in our case we have:

x = (-9 +- √(9^2 - 4*4*4))/(2*4) = (- 9 +- √17)/8

then the solutions are:

x1 = (- 9 + √17)/8 = -0.6

x2 = (-9 -  √17)/8 = -1.6