+769 Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$
+1926 First, let's combine all our like terms and move all the terms to oneside. We get
\(6x^{2}-21x-31=0\)
Now, we use the quadratic equation. We get that
\(x=\frac{-({-21})\pm \sqrt{{-21})^{2}-4\cdot {6}({-31})}}{2\cdot {6}}\)
Simplifying furher. We get 2 values for x We get
\(x=\frac{\sqrt{1185}+21}{12}\\ x=\frac{-\sqrt{1185}+21}{12}\)
Clearly, the first value of x is greater in this case, so we have
\(x=\frac{\sqrt{1185}+21}{12}\) as our final anwer.
Thanks! :)
