Question

Find all solutions to the quadratic equation -4x2+6-3

Answer 1

You have the following quadratic equation:

`-4x^2+6x-3=0`

In order to find the solution to the previous equation use the quadratic formula, as follow:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In this case, a= -4, b = 6 and c = -3.

Replace the previous values of the patameters into the quadratic formula and simplify:

`\begin{gathered} x=\frac{-(6)\pm\sqrt[]{6^2-4(-4)(-3)}}{2(-4)} \\ x=\frac{-6\pm\sqrt[]{36-48}}{-8} \\ x=\frac{-6\pm\sqrt[]{-12}}{-8} \\ x=\frac{-6\pm\sqrt[]{-3\cdot2^2}}{-8} \\ x=\frac{-6\pm2\sqrt[]{3}i}{-8} \end{gathered}`

whereHence, based on the previous result, you obtain:

`\begin{gathered} x_1=(3)/(4)+\frac{\sqrt[]{3}}{4}i \\ x_2=(3)/(4)-\frac{\sqrt[]{3}}{4}i \end{gathered}`