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

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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}

User Rujul Gandhi
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