The answer is (-9±√17)/8
This is example of quadratic equation:
ax² + bx + c = 0
which solutions are:
\(x= \frac{-b+/- \sqrt{b^{2}-4ac } }{2a}\)
Our equation 4x² = - 9x - 4 can be expressed as 4x² + 9x + 4 = 0, from which we can conclude that:
a = 4,
b = 9
c = 4
So, let's just implement that in the solution of the general quadratic equation:
\(x= \frac{-9+/- \sqrt{ 9^{2}-4*4*4 } }{2*4} =\frac{-9+/- \sqrt{ 81-64 } }{8}=\frac{-9+/- \sqrt{ 17} }{8}\)
