SOLUTION: I need to solve the quadratic formula and state if there are no real roots or not for question #14 on page #588: 3=7x-4x^2 Appreciate the help.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need to solve the quadratic formula and state if there are no real roots or not for question #14 on page #588: 3=7x-4x^2 Appreciate the help.       Log On


   

Question 76538This question is from textbook Beginning Algebra
: I need to solve the quadratic formula and state if there are no real roots or not for question #14 on page #588:
3=7x-4x^2
Appreciate the help.
 This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First get all terms to one side by subtracting 3 from both sides
-4x%5E2%2B7x-3=0
Now lets factor out a negative 1
-1%284x%5E2-7x%2B3%29=0
Now lets factor the quadratic in the parenthesis:
ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.
Error occurred executing solver 'quadratic_factoring' .


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So in other words, the quadratic -1%284x%5E2-7x%2B3%29=0 factors to -1%28%284x-3%29%28x-1%29%29=0
%284x-3%29%28x-1%29=0 Divide both sides by -1
Set each term equal to zero
4x-3=0
4x=3
x=3%2F4
x-1=0
x=1
So our solutions are:
x=3%2F4 and x=1 which are both real
We can verify this with a graph
+graph%28+300%2C+200%2C+-3%2C+2%2C+-2%2C+2%2C+-4x%5E2%2B7x-3%29+ graph of -4x%5E2%2B7x-3=0
note: you can either get help with factoring or check your work with this Quadratic Factoring Solver