$2$nd degree inequality question

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If I have an inequality of the second degree, can I solve it using the quadratic formula?

Example: $$-t^2+48t+100>500$$ Can i solve it by doing: $$-t^2+48t+(100-500)=0$$ and apply the quadratic formula to it?

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Yes you can. Either the graph will be positive between roots and negative elsewhere or vice versa. You can check that easily by putting any number except the roots(or even checking sign of limit to infinity)