Algebra Examples

$6 x^{2} = 8 x + 7$

Step 1

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

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Step 1.1

Subtract $8 x$ from both sides of the equation.

$6 x^{2} - 8 x = 7$

Step 1.2

Subtract $7$ from both sides of the equation.

$6 x^{2} - 8 x - 7 = 0$

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 $c$ .

${(- 8)}^{2} - 4 (6 \cdot - 7)$

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

$64 - 4 (6 \cdot - 7)$

Step 4.1.2

Multiply $- 4 (6 \cdot - 7)$ .

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Step 4.1.2.1

Multiply $6$ by $- 7$ .

$64 - 4 \cdot - 42$

Step 4.1.2.2

Multiply $- 4$ by $- 42$ .

$64 + 168$

Step 4.2

Add $64$ and $168$ .

$232$