# How do you find the value of the discriminant and state the type of solutions given -6x^2-6=-7x-9?

Apr 29, 2017

Solutions are two rational numbers.

#### Explanation:

$- 6 {x}^{2} - 6 = - 7 x - 9$

$\Leftrightarrow 6 {x}^{2} + 6 - 7 x - 9 = 0$

or $6 {x}^{2} - 7 x - 3 = 0$

Discriminant of quadratic equation $a {x}^{2} + b x + c = 0$ is $\Delta = {b}^{2} - 4 a c$

Here $\Delta = {\left(- 7\right)}^{2} - 4 \times 6 \times \left(- 3\right) = 49 + 72 = 121$ i.e. $\Delta > 0$ and is square of $11$

Hence, solutions are two rational numbers.

These are given by $\frac{- b \pm \sqrt{\Delta}}{2 a}$ and here these are

$\frac{7}{12} \pm \frac{11}{12}$ i.e. $\frac{3}{2}$ and $- \frac{1}{3}$

For detail see here.