Question 153542
Easiest way is to plug your answer in the original equation.
{{{2y^2-162=0}}}
{{{2(0)^2-162=0}}}
{{{-162=0}}}
Untrue.
y=0 is not a solution.
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{{{2y^2-162=0}}}
{{{2(9)^2-162=0}}}
{{{2(81)-162=0}}}
{{{162-162=0}}}
{{{0=0}}}
True.
y=9 is a solution. 
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You're missing an answer.
{{{2y^2-162=0}}}
{{{2y^2=162}}}
{{{y^2=81}}}
{{{y=0 +- 9}}}
You forgot (-9).
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Here's a graph of the function.
{{{ graph( 300, 300, -10, 10, -180, 180, 2x^2-162) }}}