Find the Discriminant 3x^2=7x+5

$3 x^{2} = 7 x + 5$

Step 1

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

Subtract $7 x$ from both sides of the equation.

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

Subtract $5$ from both sides of the equation.

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

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 $c$ .

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

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

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

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

Multiply $3$ by $- 5$ .

$49 - 4 \cdot - 15$

Multiply $- 4$ by $- 15$ .

$49 + 60$

Add $49$ and $60$ .

$109$