Solve Using the Quadratic Formula 25x^2+9=30x

$25 x^{2} + 9 = 30 x$

Step 1

Subtract $30 x$ from both sides of the equation.

$25 x^{2} + 9 - 30 x = 0$

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 $a = 25$ , $b = - 30$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{30 \pm \sqrt{{(- 30)}^{2} - 4 \cdot (25 \cdot 9)}}{2 \cdot 25}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 30$ to the power of $2$ .

$x = \frac{30 \pm \sqrt{900 - 4 \cdot 25 \cdot 9}}{2 \cdot 25}$

Multiply $- 4 \cdot 25 \cdot 9$ .

Multiply $- 4$ by $25$ .

$x = \frac{30 \pm \sqrt{900 - 100 \cdot 9}}{2 \cdot 25}$

Multiply $- 100$ by $9$ .

$x = \frac{30 \pm \sqrt{900 - 900}}{2 \cdot 25}$

Subtract $900$ from $900$ .

$x = \frac{30 \pm \sqrt{0}}{2 \cdot 25}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{30 \pm \sqrt{0^{2}}}{2 \cdot 25}$

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

$x = \frac{30 \pm 0}{2 \cdot 25}$

$30$ plus or minus $0$ is $30$ .

$x = \frac{30}{2 \cdot 25}$

Multiply $2$ by $25$ .

$x = \frac{30}{50}$

Cancel the common factor of $30$ and $50$ .

Factor $10$ out of $30$ .

$x = \frac{10 (3)}{50}$

Cancel the common factors.

Factor $10$ out of $50$ .

$x = \frac{10 \cdot 3}{10 \cdot 5}$

Cancel the common factor.

$x = \frac{10 \cdot 3}{10 \cdot 5}$

Rewrite the expression.

$x = \frac{3}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{5}$ Double roots