# Find the largest root of 2 x 2 </msup> + 3 x + 6 = 7 x <msqrt>

Find the largest root of
$2{x}^{2}+3x+6=7x\sqrt{x+2}$
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iskakanjulc
Let $y=\sqrt{x+2}$. Then the equation becomes
$2{x}^{2}-7xy+3{y}^{2}=0$
Which you can factor as a quadratic
$\left(2x-y\right)\left(x-3y\right)=0$
Or (using $x={y}^{2}-2$)
$\left(2{y}^{2}-y-4\right)\left({y}^{2}-3y-2\right)=0$
Find the largest root of each quadratic, then the overall largest root, then get back to x.