Solve Using the Quadratic Formula 5x^2-2x+16=4x^2+6x

$5 x^{2} - 2 x + 16 = 4 x^{2} + 6 x$

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 $4 x^{2}$ from both sides of the equation.

$5 x^{2} - 2 x + 16 - 4 x^{2} = 6 x$

Subtract $6 x$ from both sides of the equation.

$5 x^{2} - 2 x + 16 - 4 x^{2} - 6 x = 0$

Simplify $5 x^{2} - 2 x + 16 - 4 x^{2} - 6 x$ .

Subtract $4 x^{2}$ from $5 x^{2}$ .

$x^{2} - 2 x + 16 - 6 x = 0$

Subtract $6 x$ from $- 2 x$ .

$x^{2} - 8 x + 16 = 0$

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 $a = 1$ , $b = - 8$ , and $c = 16$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 16)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 16}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 16$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 16}}{2 \cdot 1}$

Multiply $- 4$ by $16$ .

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

Subtract $64$ from $64$ .

$x = \frac{8 \pm \sqrt{0}}{2 \cdot 1}$

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

$x = \frac{8 \pm \sqrt{0^{2}}}{2 \cdot 1}$

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

$x = \frac{8 \pm 0}{2 \cdot 1}$

$8$ plus or minus $0$ is $8$ .

$x = \frac{8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8}{2}$

Divide $8$ by $2$ .

$x = 4$

Step 5

The final answer is the combination of both solutions.

$x = 4$ Double roots