# Appendix B - Exercise Set - Page 981: 42

$x = +0.2$ or $x =+4$

#### Work Step by Step

$\frac{5x^2}{6} - \frac{7x}{2} + \frac{2}{3} = 0$ Step 1: Clear the equation from fractions. $6(\frac{5x^2}{6} - \frac{7x}{2} + \frac{2}{3} )= 6\times0$ Step 2: Use the distribute property. $5x^2 - 21x + 4 = 0$ Step 3: is not needed since no simplifying can be done on either side of the equation. $5x^2 - 21x + 4 = 0$ Step 4: The equation is quadratic. Step 5: Rewrite the equation in standard form. $5x^2 -21x+ 4 = 0$ Step 6: Factor. $(5x -1)(x -4) = 0$ Step 7: Set each factor equal to 0. $5x -1 = 0$ or $x -4 = 0$ Solve each equation. $5x = +1$ or $x =+4$ $x = +0.2$ or $x =+4$

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