Question 751745
{{{ 16x^2-72x=-85 }}}
I don't know which method they want you to use, but 
I can try completing the square
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First, divide both sides by {{{ 16 }}}
{{{ x^2 - (9/2)*x = -85/16 }}}
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Take 1/2 of the coefficient of {{{ x }}},
square it, and add it to both sides
{{{ x^2 - (9/2)*x + (9/4)^2 = -85/16 + (9/4)^2 }}}
{{{ x^2 - (9/2)*x + 81/16 = -85/16 + 81/16 }}}
{{{ x^2 - (9/2)*x + 81/16 = -4/16 }}}
{{{ ( x - 9/4 )^2 = ( 1/2)^2 * i^2 }}}
Take the square root of both sides
{{{ x - 9/4 = (1/2)*i }}}
{{{ x = ( 9 + 2i ) / 4 }}}
and, also
{{{ x = ( 9 - 2i ) / 4 }}}
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Here's the plot:
{{{ graph( 500, 500, -2, 5, -2, 8, 16x^2 - 72x + 85 ) }}}
Since it doesn't contact the x-axis, there are no real roots