Finite Math Examples

$4 x^{2} = 11 x + 3$

Step 1

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

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Step 1.1

Subtract $11 x$ from both sides of the equation.

$4 x^{2} - 11 x = 3$

Step 1.2

Subtract $3$ from both sides of the equation.

$4 x^{2} - 11 x - 3 = 0$

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 $c$ .

${(- 11)}^{2} - 4 (4 \cdot - 3)$

Step 4

Evaluate the result to find the discriminant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Raise $- 11$ to the power of $2$ .

$121 - 4 (4 \cdot - 3)$

Step 4.1.2

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

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Step 4.1.2.1

Multiply $4$ by $- 3$ .

$121 - 4 \cdot - 12$

Step 4.1.2.2

Multiply $- 4$ by $- 12$ .

$121 + 48$

Step 4.2

Add $121$ and $48$ .

$169$