Question 554524
This is determined by what is called the " discriminant "
This is {{{ b^2 - 4a*c }}} in the formula for the roots
which is {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this case:
{{{ 2x^2-7x+9=x+1 }}}
{{{ 2x^2 -7x - x+ 9 - 1 = 0 }}}
{{{ 2x^2 - 8x + 8 = 0 }}}
{{{ x^2 - 4x + 4 = 0 }}}
{{{ a = 1 }}}
{{{ b = -4 }}}
{{{ c = 4 }}}
{{{ b^2 - 4a*c = (-4)^2 - 4*1*4 }}}
{{{ b^2 - 4a*c = 16 - 16 }}}
The discriminant is zero, which means there is 1 solution,
which is called a double root. Here's a plot of the
equation. Notice it touches the x-axis at 1 point
{{{ graph( 400, 400, -5, 5, -5, 5, x^2 - 4x + 4 ) }}}