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# Algebra

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Find all solutions to the equation 6x^2 - 31x + 42 = 0. If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in a + bi form.

Jan 24, 2022

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To get the solutions, we must first apply the quadratic formula to the equation above.

The quadratic formula is: $$-b {+\over} \sqrt{b^2 - 4ac}\over2a$$ where $$a$$ is the coefficient of $$x^2$$$$b$$ is the coefficient of $$x$$, and $$c$$ is the constant.

Now to apply it.

$$31 {+\over} \sqrt{961 - 1008}\over12$$

Now we have the two solutions.

Here they are:

$$31 + i\sqrt{47}\over12$$ , $$31 - i\sqrt{47}\over12$$

Jan 24, 2022