Question

Solve for x:

3x2-2x-83=0

Answer 1

We have been given, 3x2-2x-83=0

Now we also know that for an equation `ax^2+bx+c=0`, the discriminant is given by the following equation: `D=b^2-4ac`

Now, according to the equation given to us, we have,`a=sqrt3`, b = −2 and`c=-8sqrt3`.

Therefore, the discriminant is given as,

\[D = \left( - 2 \right)^2 - 4 \times \sqrt{3} \times \left( - 8\sqrt{3} \right)\]

\[ = 4 + 96 = 100\]

Now, the roots of an equation is given by the following equation,

`x=(-b\pmsqrtD)/(2a)`

Therefore, the roots of the equation are given as follows,

\[x = \frac{2 + 10}{2\sqrt{3}} = \frac{12}{2\sqrt{3}} = \frac{6}{\sqrt{3}}\]

Now we solve both cases for the two values of x. So, we have,

\[x = \frac{2 + 10}{2\sqrt{3}} = \frac{12}{2\sqrt{3}} = \frac{6}{\sqrt{3}}\]

Also,

\[x = \frac{2 - 10}{2\sqrt{3}} = \frac{- 8}{2\sqrt{3}} = \frac{- 4}{\sqrt{3}}\]

Therefore, value of x will be 

\[\frac{6}{\sqrt{3}} and \frac{- 4}{\sqrt{3}}\]