solve quadratic equation 6X^2+7X+10

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Write Quadratic Equation: Write down the quadratic equation. We have the quadratic equation 6X^2 + 7X + 10 = 0.Identify Coefficients: Identify the coefficients of the quadratic equation. The coefficients are a = 6, b = 7, and c = 10.Check Factorization: Check if the quadratic can be factored easily. The quadratic equation 6X^2 + 7X + 10 does not factor easily because there are no two integers that multiply to 6*10 (60) and add up to 7. Therefore, we will use the quadratic formula to find the solutions.Recall Quadratic Formula: Recall the quadratic formula. The quadratic formula is X = (-b ± √(b^2 - 4ac)) / (2a).Substitute Coefficients: Substitute the coefficients into the quadratic formula. Substitute a = 6, b = 7, and c = 10 into the formula to get X = (-(7) ± √((7)^2 - 4(6)(10))) / (2(6)).Simplify Square Root: Simplify under the square root. Calculate the discriminant: (7)^2 - 4(6)(10) = 49 - 240 = -191.Negative Discriminant: Since the discriminant is negative, the solutions will be complex numbers. We have X = (-7 ± √(-191)) / 12.Complex Number Solutions: Write the solutions in terms of complex numbers. The solutions are X = (-7 + √(-191)) / 12 and X = (-7 - √(-191)) / 12, which can be written as X = -7/12 + √(191)i/12 and X = -7/12 - √(191)i/12.

solve quadratic equation $6X^2+7X+10$

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solve quadratic equation $6X^2+7X+10$