Find the Discriminant -3x^2+8x+17=-4x^2+1

$- 3 x^{2} + 8 x + 17 = - 4 x^{2} + 1$

Move all terms to the left side of the equation and simplify.

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

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

$- 3 x^{2} + 8 x + 17 + 4 x^{2} = 1$

Subtract $1$ from both sides of the equation.

$- 3 x^{2} + 8 x + 17 + 4 x^{2} - 1 = 0$

Simplify $- 3 x^{2} + 8 x + 17 + 4 x^{2} - 1$ .

Add $- 3 x^{2}$ and $4 x^{2}$ .

$x^{2} + 8 x + 17 - 1 = 0$

Subtract $1$ from $17$ .

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

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

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

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

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

Evaluate the result to find the discriminant.

Simplify each term.

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

$64 - 4 (1 \cdot 16)$

Multiply $16$ by $1$ .

$64 - 4 \cdot 16$

Multiply $- 4$ by $16$ .

$64 - 64$

Subtract $64$ from $64$ .

$0$