Solve for x 2(2x-1)=5x^2

$2 (2 x - 1) = 5 x^{2}$

Simplify $2 (2 x - 1)$ .

Start simplifying.

$0 + 0 + 2 (2 x - 1) = 5 x^{2}$

Simplify by adding zeros.

$2 (2 x - 1) = 5 x^{2}$

Apply the distributive property.

$2 (2 x) + 2 \cdot - 1 = 5 x^{2}$

Multiply.

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 1 = 5 x^{2}$

Multiply $2$ by $- 1$ .

$4 x - 2 = 5 x^{2}$

Subtract $5 x^{2}$ from both sides of the equation.

$4 x - 2 - 5 x^{2} = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - 5$ , $b = 4$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

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

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 5 \cdot - 2}}{2 \cdot - 5}$

Multiply $- 4$ by $- 5$ .

$x = \frac{- 4 \pm \sqrt{16 + 20 \cdot - 2}}{2 \cdot - 5}$

Multiply $20$ by $- 2$ .

$x = \frac{- 4 \pm \sqrt{16 - 40}}{2 \cdot - 5}$

Subtract $40$ from $16$ .

$x = \frac{- 4 \pm \sqrt{- 24}}{2 \cdot - 5}$

Rewrite $- 24$ as $- 1 (24)$ .

$x = \frac{- 4 \pm \sqrt{- 1 \cdot 24}}{2 \cdot - 5}$

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$x = \frac{- 4 \pm \sqrt{- 1} \cdot \sqrt{24}}{2 \cdot - 5}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 4 \pm i \cdot \sqrt{24}}{2 \cdot - 5}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \frac{- 4 \pm i \cdot \sqrt{4 (6)}}{2 \cdot - 5}$

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

$x = \frac{- 4 \pm i \cdot \sqrt{2^{2} \cdot 6}}{2 \cdot - 5}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm i \cdot (2 \sqrt{6})}{2 \cdot - 5}$

Move $2$ to the left of $i$ .

$x = \frac{- 4 \pm 2 i \sqrt{6}}{2 \cdot - 5}$

Multiply $2$ by $- 5$ .

$x = \frac{- 4 \pm 2 i \sqrt{6}}{- 10}$

Simplify $\frac{- 4 \pm 2 i \sqrt{6}}{- 10}$ .

$x = \frac{2 \pm i \sqrt{6}}{5}$

The final answer is the combination of both solutions.

$x = \frac{2 + i \sqrt{6}}{5}, \frac{2 - i \sqrt{6}}{5}$

Solve for x 2(2x-1)=5x^2

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