Solve Using the Quadratic Formula (x-8)(5x-6)=0

$(x - 8) (5 x - 6) = 0$

Step 1

Simplify the left side.

Simplify $(x - 8) (5 x - 6)$ .

Expand $(x - 8) (5 x - 6)$ using the FOIL Method.

Apply the distributive property.

$x (5 x - 6) - 8 (5 x - 6) = 0$

Apply the distributive property.

$x (5 x) + x \cdot - 6 - 8 (5 x - 6) = 0$

Apply the distributive property.

$x (5 x) + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 x \cdot x + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x) + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = 0$

Multiply $x$ by $x$ .

$5 x^{2} + x \cdot - 6 - 8 (5 x) - 8 \cdot - 6 = 0$

Move $- 6$ to the left of $x$ .

$5 x^{2} - 6 \cdot x - 8 (5 x) - 8 \cdot - 6 = 0$

Multiply $5$ by $- 8$ .

$5 x^{2} - 6 x - 40 x - 8 \cdot - 6 = 0$

Multiply $- 8$ by $- 6$ .

$5 x^{2} - 6 x - 40 x + 48 = 0$

Subtract $40 x$ from $- 6 x$ .

$5 x^{2} - 46 x + 48 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 5$ , $b = - 46$ , and $c = 48$ into the quadratic formula and solve for $x$ .

$\frac{46 \pm \sqrt{{(- 46)}^{2} - 4 \cdot (5 \cdot 48)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 46$ to the power of $2$ .

$x = \frac{46 \pm \sqrt{2116 - 4 \cdot 5 \cdot 48}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 48$ .

Multiply $- 4$ by $5$ .

$x = \frac{46 \pm \sqrt{2116 - 20 \cdot 48}}{2 \cdot 5}$

Multiply $- 20$ by $48$ .

$x = \frac{46 \pm \sqrt{2116 - 960}}{2 \cdot 5}$

Subtract $960$ from $2116$ .

$x = \frac{46 \pm \sqrt{1156}}{2 \cdot 5}$

Rewrite $1156$ as $34^{2}$ .

$x = \frac{46 \pm \sqrt{34^{2}}}{2 \cdot 5}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{46 \pm 34}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{46 \pm 34}{10}$

Simplify $\frac{46 \pm 34}{10}$ .

$x = \frac{23 \pm 17}{5}$

Step 5

The final answer is the combination of both solutions.

$x = 8, \frac{6}{5}$

Solve Using the Quadratic Formula (x-8)(5x-6)=0

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