# What are the solution(s) of 5 - 10x - 3x^2 = 0?

Oct 21, 2015

x_(1,2) = -5/3 ∓ 2/3sqrt(10)

#### Explanation:

For a general form quadratic equation

$\textcolor{b l u e}{a {x}^{2} + b x + c = 0}$

you can find its roots by using the quadratic formula

$\textcolor{b l u e}{{x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}}$

The quadratic equation you were given looks like this

$5 - 10 x - 3 {x}^{2} = 0$

Rearrange it to match the general form

$- 3 {x}^{2} - 10 x + 5 = 0$

In your case, you have $a = - 3$, $b = - 10$, and $c = 5$. This means that the two roots will take the form

${x}_{1 , 2} = \frac{- \left(- 10\right) \pm \sqrt{{\left(- 10\right)}^{2} - 4 \cdot \left(- 3\right) \cdot \left(5\right)}}{2 \cdot \left(- 3\right)}$

${x}_{1 , 2} = \frac{10 \pm \sqrt{100 + 60}}{\left(- 6\right)}$

x_(1,2) = (10 +- sqrt(160))/((-6)) = -5/3 ∓ 2/3sqrt(10)

The two solutions will thus be

${x}_{1} = - \frac{5}{3} - \frac{2}{3} \sqrt{10} \text{ }$ and $\text{ } {x}_{2} = - \frac{5}{3} + \frac{2}{3} \sqrt{10}$