$$ 6 x^{2}=8 x+7 $$ What is the discriminant, $$ b^{2}-4 a c ? $$ $$ \square $$ (Simplify your answer.)

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The discriminant is 232. To find the discriminant of the quadratic equation $$ 6x^2 = 8x + 7 $$, we first need to rewrite it in the standard form $$ ax^2 + bx + c = 0 $$. Starting with the given equation: $$ 6x^2 - 8x - 7 = 0 $$ Here, we can identify the coefficients: - $$ a = 6 $$ - $$ b = -8 $$ - $$ c = -7 $$ The discriminant $$ D $$ is given by the formula: $$ D = b^2 - 4ac $$ Now, we can substitute the values of $$ a $$, $$ b $$, and $$ c $$ into the formula: $$ D = (-8)^2 - 4 \cdot 6 \cdot (-7) $$ Calculating $$ (-8)^2 $$: $$ (-8)^2 = 64 $$ Now calculating $$ 4 \cdot 6 \cdot (-7) $$: $$ 4 \cdot 6 = 24 $$ $$ 24 \cdot (-7) = -168 $$ Now substituting back into the discriminant formula: $$ D = 64 - (-168) $$ $$ D = 64 + 168 $$ $$ D = 232 $$ Thus, the discriminant is: $$ \boxed{232} $$

\( 6 x^{2}=8 x+7 \) What is the discriminant, \( b^{2}-4 a c ? \) \( \square \) (Simplify your answer.)

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\( 6 x^{2}=8 x+7 \) What is the discriminant, \( b^{2}-4 a c ? \) \( \square \) (Simplify your answer.)

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