# How do you solve x(2x+1)=-4 using the quadratic formula?

Jul 17, 2017

We must get the equation into the form of $a {x}^{2} + b x + c = 0$

#### Explanation:

$x \left(2 x + 1\right) = - 4 \iff 2 {x}^{2} + x + 4 = 0$

So now $a = 2 , b = 1 , c = 4$

from the formula we know

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} = \frac{- 1 \pm \sqrt{1 - 32}}{4}$

so we see that the equation has no real solutions, but it has comple ones.

which are

x=-1/4+-isqrt(31/16