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Find all solutions to the equation 6x^2 - 31x + 40 = 4x^2 - 28x + 30. 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.

 Jun 4, 2022
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\(6x^2-31x+40=4x^2-28x+30\)

 

Moving all the terms to the left, we have \(2x^2-3x+10=0\).

 

By the quadratic equation, we know that the solutions are \(\frac{3+\sqrt{9-4\cdot2\cdot10}}{4}=\frac{3+i\sqrt{71}}{4}\) and \(\frac{3-\sqrt{9-4\cdot2\cdot10}}{4}=\frac{3-i\sqrt{71}}{4}\).

 Jun 6, 2022
edited by RainbowSquirrel53  Jun 6, 2022

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