Solve Using the Quadratic Formula -13x^2-9x+4=5+2x^2-x

$- 13 x^{2} - 9 x + 4 = 5 + 2 x^{2} - x$

Step 1

Move all terms to the left side of the equation and simplify.

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

Subtract $5$ from both sides of the equation.

$- 13 x^{2} - 9 x + 4 - 5 = 2 x^{2} - x$

Subtract $2 x^{2}$ from both sides of the equation.

$- 13 x^{2} - 9 x + 4 - 5 - 2 x^{2} = - x$

Add $x$ to both sides of the equation.

$- 13 x^{2} - 9 x + 4 - 5 - 2 x^{2} + x = 0$

Simplify $- 13 x^{2} - 9 x + 4 - 5 - 2 x^{2} + x$ .

Subtract $2 x^{2}$ from $- 13 x^{2}$ .

$- 15 x^{2} - 9 x + 4 - 5 + x = 0$

Add $- 9 x$ and $x$ .

$- 15 x^{2} - 8 x + 4 - 5 = 0$

Subtract $5$ from $4$ .

$- 15 x^{2} - 8 x - 1 = 0$

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 $a = - 15$ , $b = - 8$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (- 15 \cdot - 1)}}{2 \cdot - 15}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 15 \cdot - 1}}{2 \cdot - 15}$

Multiply $- 4 \cdot - 15 \cdot - 1$ .

Multiply $- 4$ by $- 15$ .

$x = \frac{8 \pm \sqrt{64 + 60 \cdot - 1}}{2 \cdot - 15}$

Multiply $60$ by $- 1$ .

$x = \frac{8 \pm \sqrt{64 - 60}}{2 \cdot - 15}$

Subtract $60$ from $64$ .

$x = \frac{8 \pm \sqrt{4}}{2 \cdot - 15}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{8 \pm \sqrt{2^{2}}}{2 \cdot - 15}$

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

$x = \frac{8 \pm 2}{2 \cdot - 15}$

Multiply $2$ by $- 15$ .

$x = \frac{8 \pm 2}{- 30}$

Simplify $\frac{8 \pm 2}{- 30}$ .

$x = \frac{4 \pm 1}{- 15}$

Move the negative in front of the fraction.

$x = - \frac{4 \pm 1}{15}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{1}{3}, - \frac{1}{5}$

Solve Using the Quadratic Formula -13x^2-9x+4=5+2x^2-x

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