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Q. 30

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Found in: Page 29

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.$5{x}^{2}=13x+6$

The required solution is $x=-\frac{2}{5},3$ and the graph of the solution is shown below:

See the step by step solution

## Step 1. Given information.

We have:

$5{x}^{2}=13x+6$

## Step 2. Solve the equation algebraically.

The equation is $5{x}^{2}=13x+6$.

$5{x}^{2}-13x-6=0$

For a quadratic equation of the form $a{x}^{2}+bx+c=0$ the solutions are:

${x}_{1, 2}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$

For $a=5, b=-13, c=-6$

${x}_{1, 2}=\frac{-\left(-13\right)±\sqrt{{\left(-13\right)}^{2}-4· 5\left(-6\right)}}{2· 5}\phantom{\rule{0ex}{0ex}}{x}_{1, 2}=\frac{-\left(-13\right)± 17}{2· 5}\phantom{\rule{0ex}{0ex}}x=3,-\frac{2}{5}$

## Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x=-\frac{2}{5},3$.

Draw the graph of the equation $5{x}^{2}=13x+6$ using the graphing utility: