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Solve the following equation for x: 9x^2...

Solve the following equation for x: `9x^2 - 9 (p+q)x + (2 p^2 + 5pq + 2 q^2) = 0`

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`9x^2-9(p+q)x+2p^2+5pq+2q^2=6`
`9x^2-9(p+q)x+2p^2+4pq+pq+2q^2=0`
`9x^2-9(p+q)+(2p+q)(p+2q)=0`
`x=(9(p+q)pmsqrt(81p^2+162pq+81q^2)-72p^2-72q^2-180pq)/18`
`x=(9(p+q)pm(3p-3q))/18`
`x=(9p+9q+3p-3q)/18=(12p+6q)/18=(2p)/3+q/3`
`x=(9p+9q-3p+3q)/18=(6p+12q)/18=p/3+(2q)/3`.
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