Find the Roots (Zeros) -18x+5=-15x^2+4x

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

Move all terms containing $x$ to the left side of the equation.

Add $18 x$ to both sides of the equation.

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

Add $4 x$ and $18 x$ .

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

Step 3

Subtract $5$ from both sides of the equation.

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

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

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 6

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 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.18548866 \dots, 0.28117800 \dots$

Step 8

Find the Roots (Zeros) -18x+5=-15x^2+4x

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