Can anyone explain the solutions of quadratics to me. its a little confusing. it would a lot.

A quadratic equation is one that contains the term x² somewhere in the equation. They could look like:

x²=25
x²+10x+24=0
x(x-1)=6      [this one's in disguise, when you expand the bracket there's an x²]

Unlike most linear equations, quadratic equations can either have two possible solutions, one solution or no solutions depending on the individual quadratic.

The solutions of a quadratic equation are when the curve crosses the x-axis, because a quadratic curve is u-shaped, if the bottom dips below the x-axis, there are two solutions, if it touches there is one, and if it is completely above the x-axis then there are none.

There are three ways to solve a quadratic equation, the first is factorising, this is when you 'reverse expand' and put the brackets back in:

x²+10x+24 = 0 gives (x+6)(x+4) = 0
therefore the solutions to this equation are x=-6 and x=-4

The second way is to complete the square, this can be a bit easier as there is a set method. You halve the number in front of the x and put this in brackets with (x + ___)² and then take away the number squared. For example:
x²+10x+24 = 0
[halve 10, put it in brackets, take away 5 squared]: (x+5)² - 25 +24 = 0
(x+5)²=1
x=-51 ==> x=-6 or x=-4

The third way is the easiest but looks scariest, the quadratic formula is
This works for a quadratic of the form ax²+bx+c = 0, our example is x²+10x+24=0 so by comparing these we see [a=1, b=10, c=24] and then we just put these numbers into the formula to get

so x=-6 or x=-4

This is a very brief overview, if you need any more help with anything specific then leave it in the comments and I'll do my best to explain. Also http://www.mathsisfun.com/algebra/quadratic-equation.html this is a very, very good website to help you understand everything I've just said and more!
(I should point out I do not own this website and all credit goes to Rod Pierce for writing this page.)

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !