SOLUTION: Please help me with this problem and please show me how to solve it. Thank you Solve equation using the quadratic formula 5z^2 = 2z + 3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me with this problem and please show me how to solve it. Thank you Solve equation using the quadratic formula 5z^2 = 2z + 3      Log On


   

Question 169893: Please help me with this problem and please show me how to solve it. Thank you
Solve equation using the quadratic formula
5z^2 = 2z + 3
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Start by moving all the terms to one side:
5z^2 = 2z + 3
Subtracting both sides by 2z+3:
5z^2 - 2z - 3 = 0
.
Always attempt to factor first, then failing that use the quadratic equation.
.
In this case, you must use the quadratic equation. Doing so will yield:
z = {1, -0.6}
.
Details of quadratic below:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation az%5E2%2Bbz%2Bc=0 (in our case 5z%5E2%2B-2z%2B-3+=+0) has the following solutons:

z%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A5%2A-3=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca.

z%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C5+=+1
z%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C5+=+-0.6

Quadratic expression 5z%5E2%2B-2z%2B-3 can be factored:
5z%5E2%2B-2z%2B-3+=+5%28z-1%29%2A%28z--0.6%29
Again, the answer is: 1, -0.6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B-3+%29