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In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
There are many different formulas and equations for algebra.
I'm going to differ on many thoughts. I believe that geometry is MUCH easier than Algebra 1 - especially the 2nd semester of algebra 1 which a good chunk of time was spent on factoring and quadratic equations. The Algebra used in geometry is fairly basic - lots of 1 and 2 step equations. By the second semester you will get into some more complicated algorthims when dealing with area and surface area but that is about as difficult as it will get. I bet you'll feel that your algebra skills increase after looking at things geometrically.
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If they are quadratic equations then if their discriminant is less than zero then they have no solutions