Answer
$x_{1}=\dfrac{-5+\sqrt{13}}{2}\approx -0.697$
$x_{2}=\dfrac{-5-\sqrt{13}}{2}\approx-4.30$
Work Step by Step
We have to solve $x^2+5x+3=0.$ Let's find the discriminant. The quadratic equation in its standard form is $ax^2 + bx + c = 0$.
$$D=b^2-4ac$$
In our case
$$D=25-4\cdot1\cdot3=25-12=13>0$$
We have two solutions.
$$x_{1}=\dfrac{-b+\sqrt D}{2a}=\dfrac{-5+\sqrt{13}}{2}\approx -0.697$$
$$x_{2}=\dfrac{-b-\sqrt D}{2a}=\dfrac{-5-\sqrt{13}}{2}\approx-4.30$$
