Find the Sum and Product of the Roots of the Quadratic Equation 8x^2=6x+9

$8 x^{2} = 6 x + 9$

Step 1

Find $a$ , $b$ , and $c$ .

Move all the expressions to the left side of the equation.

Subtract $6 x$ from both sides of the equation.

$8 x^{2} - 6 x = 9$

Subtract $9$ from both sides of the equation.

$8 x^{2} - 6 x - 9 = 0$

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 8$ , $b = - 6$ , $c = - 9$

Step 2

Substitute the values into the sum of roots formula $- \frac{b}{a}$ .

Cancel the common factor of $6$ and $8$ .

Factor $2$ out of $6$ .

$\frac{2 (3)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{2 \cdot 3}{2 \cdot 4}$

Cancel the common factor.

$\frac{2 \cdot 3}{2 \cdot 4}$

Rewrite the expression.

$\frac{3}{4}$

Step 3

Substitute the values into the product of roots formula $\frac{c}{a}$ .

Move the negative in front of the fraction.

$- \frac{9}{8}$

Step 4

List the results.

Sum of the roots is $\frac{3}{4}$

Product of the roots is $- \frac{9}{8}$