Find the Discriminant 0=-x^2+4x+1

$0 = - x^{2} + 4 x + 1$

Step 1

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

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

$x^{2} = 4 x + 1$

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

$x^{2} - 4 x = 1$

Subtract $1$ from both sides of the equation.

$x^{2} - 4 x - 1 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 4)}^{2} - 4 (1 \cdot - 1)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$16 - 4 (1 \cdot - 1)$

Multiply $- 4 (1 \cdot - 1)$ .

Multiply $- 1$ by $1$ .

$16 - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$16 + 4$

Add $16$ and $4$ .

$20$