Question 1209215
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Find the largest value of x such that 3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.
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Collect all the terms of the equation in its left side

    3x^2 + 17x + 15 - 2x^2 - 21x - 12 + 5x^2 - 17x - 34 = 0.


Group like terms

    (3x^2 - 2x^2 + 5x^2) + (17x - 21x - 17x) + (15 - 12 - 34).


Combine like terms

    6x^2 - 21x - 31 = 0.


Use the quadratic formula to find the roots

    {{{x[1,2]}}} = {{{(21 +- sqrt((-21)^2 - 4*6*(-31)))/(2*6)}}} = {{{(21 +- sqrt(1185))/12}}}.


The greatest root is  {{{(21 + sqrt(1185))/12}}} = 4.618652413  (approximate value).


<U>ANSWER</U>.  The greatest root is  {{{(21 + sqrt(1185))/12}}}, or about 4.618652413  (approximate value).
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Solved.