Find the Discriminant 2x^2=-10x+9

$2 x^{2} = - 10 x + 9$

Step 1

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

Add $10 x$ to both sides of the equation.

$2 x^{2} + 10 x = 9$

Subtract $9$ from both sides of the equation.

$2 x^{2} + 10 x - 9 = 0$

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 $c$ .

$10^{2} - 4 (2 \cdot - 9)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $10$ to the power of $2$ .

$100 - 4 (2 \cdot - 9)$

Multiply $- 4 (2 \cdot - 9)$ .

Multiply $2$ by $- 9$ .

$100 - 4 \cdot - 18$

Multiply $- 4$ by $- 18$ .

$100 + 72$

Add $100$ and $72$ .

$172$