Question 1067603
{{{y=-x^2+19x-90}}} intersects the x-axis (the {{{y=0}}} line) when {{{y=0}}} ,
so you have to solve the equation
{{{-x^2+19x-90=0}}} .
Since I do not like that minus sign at the left end,
I would multiply both sides of the equal sign times {{{-1}}} to get
the equivalent equation {{{x^2-19x+90=0}}} .
Then I would factor that polynomial as
{{{(x-10)(x-9)=0}}} ,
and that would tell me that the solutions of the equation are
the solution of {{{x-10=0}}}  and
the solution of {{{x-9=0}}} .
Those solutions are 
{{{highlight(x=9)}}} and {{{highlight(x=10)}}} .