Find the Discriminant 5x^2-4x+1=3x+4

$5 x^{2} - 4 x + 1 = 3 x + 4$

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 $3 x$ from both sides of the equation.

$5 x^{2} - 4 x + 1 - 3 x = 4$

Subtract $4$ from both sides of the equation.

$5 x^{2} - 4 x + 1 - 3 x - 4 = 0$

Simplify $5 x^{2} - 4 x + 1 - 3 x - 4$ .

Subtract $3 x$ from $- 4 x$ .

$5 x^{2} - 7 x + 1 - 4 = 0$

Subtract $4$ from $1$ .

$5 x^{2} - 7 x - 3 = 0$

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 $c$ .

${(- 7)}^{2} - 4 (5 \cdot - 3)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 7$ to the power of $2$ .

$49 - 4 (5 \cdot - 3)$

Multiply $- 4 (5 \cdot - 3)$ .

Multiply $5$ by $- 3$ .

$49 - 4 \cdot - 15$

Multiply $- 4$ by $- 15$ .

$49 + 60$

Add $49$ and $60$ .

$109$