Find the Discriminant 4x^2-15x+16=3x^2-7x

$4 x^{2} - 15 x + 16 = 3 x^{2} - 7 x$

Move all terms to the left side of the equation and simplify.

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

Subtract $3 x^{2}$ from both sides of the equation.

$4 x^{2} - 15 x + 16 - 3 x^{2} = - 7 x$

Add $7 x$ to both sides of the equation.

$4 x^{2} - 15 x + 16 - 3 x^{2} + 7 x = 0$

Simplify $4 x^{2} - 15 x + 16 - 3 x^{2} + 7 x$ .

Subtract $3 x^{2}$ from $4 x^{2}$ .

$x^{2} - 15 x + 16 + 7 x = 0$

Add $- 15 x$ and $7 x$ .

$x^{2} - 8 x + 16 = 0$

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 8)}^{2} - 4 (1 \cdot 16)$

Evaluate the result to find the discriminant.

Simplify each term.

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

$64 - 4 (1 \cdot 16)$

Multiply $16$ by $1$ .

$64 - 4 \cdot 16$

Multiply $- 4$ by $16$ .

$64 - 64$

Subtract $64$ from $64$ .

$0$