# Solve for all complex solutions: 4m^2+8m+5=0 how do I solve?

$m = - 1 + \frac{i}{2} \setminus \mathmr{and} - 1 - \frac{i}{2}$
Just use quadratic formula $m = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
Here we have $a = 4 , b = 8 , c = 5$ So plug these:
$m = \frac{- 8 \pm \sqrt{{8}^{2} - 4 \left(4\right) \left(5\right)}}{2 \cdot 4} = \frac{- 8 \pm \sqrt{64 - 80}}{8} = \frac{- 8 \pm \sqrt{- 16}}{8} = \frac{- 8 \pm 4 i}{8} = - 1 \pm \frac{i}{2}$