How to solve -3r2 plus 21r plus 24 equals?

Answer 1

OK, this looks like a quadratic equation, which means a polynomial whose highest power is two:

-3r^2 + 21r + 24 = 0

The general form for a quadratic equation is

ax^2 + bx + c = 0

and the general solution is given by the quadratic formula:

x = [ -b +- sqrt(b^2 - 4ac) ] / 2a

Because a quadratic equation is second order, it has two solutions, or roots. The +- symbol means to use the "+" sign first, and then use the "-" sign. It is read as "plus or minus."

So, if we replace the x with your r, and the coefficients, a, b, c, with the ones from your equation, we get for a solution:

r = [-21 +- sqrt(21^2 - 4 * -3 * 24) ] / 2 * -3

When you do the arithmetic using the "+" sign, you get -1 for the first root, and using the "-" sign you get 8 for the second root.

So, the solutions are -1 and 8, which you can verify by plugging either of these into the original equation.