Solve Using the Quadratic Formula -18x+5=-15x^2+4x

$- 18 x + 5 = - 15 x^{2} + 4 x$

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.

Add $15 x^{2}$ to both sides of the equation.

$- 18 x + 5 + 15 x^{2} = 4 x$

Subtract $4 x$ from both sides of the equation.

$- 18 x + 5 + 15 x^{2} - 4 x = 0$

Subtract $4 x$ from $- 18 x$ .

$- 22 x + 5 + 15 x^{2} = 0$

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 $a = 15$ , $b = - 22$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{22 \pm \sqrt{{(- 22)}^{2} - 4 \cdot (15 \cdot 5)}}{2 \cdot 15}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 22$ to the power of $2$ .

$x = \frac{22 \pm \sqrt{484 - 4 \cdot 15 \cdot 5}}{2 \cdot 15}$

Multiply $- 4 \cdot 15 \cdot 5$ .

Multiply $- 4$ by $15$ .

$x = \frac{22 \pm \sqrt{484 - 60 \cdot 5}}{2 \cdot 15}$

Multiply $- 60$ by $5$ .

$x = \frac{22 \pm \sqrt{484 - 300}}{2 \cdot 15}$

Subtract $300$ from $484$ .

$x = \frac{22 \pm \sqrt{184}}{2 \cdot 15}$

Rewrite $184$ as $2^{2} \cdot 46$ .

Factor $4$ out of $184$ .

$x = \frac{22 \pm \sqrt{4 (46)}}{2 \cdot 15}$

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

$x = \frac{22 \pm \sqrt{2^{2} \cdot 46}}{2 \cdot 15}$

Pull terms out from under the radical.

$x = \frac{22 \pm 2 \sqrt{46}}{2 \cdot 15}$

Multiply $2$ by $15$ .

$x = \frac{22 \pm 2 \sqrt{46}}{30}$

Simplify $\frac{22 \pm 2 \sqrt{46}}{30}$ .

$x = \frac{11 \pm \sqrt{46}}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11 \pm \sqrt{46}}{15}$

Decimal Form:

$x = 1.18548866 \dots, 0.28117800 \dots$