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Discriminant of $$$\frac{5 \left(2 x - 1\right)^{2}}{3} = 125$$$
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Your Input
Find the discriminant of $$$\frac{5 \left(2 x - 1\right)^{2}}{3} = 125$$$.
Solution
Rewrite the equation: $$$\frac{5 \left(2 x - 1\right)^{2}}{3} = 125$$$ becomes $$$\frac{5 \left(2 x - 1\right)^{2}}{3} - 125 = 0$$$.
The discriminant of the quadratic equation $$$a x^{2} + b x + c = 0$$$ is $$$D = b^{2} - 4 a c$$$.
Our equation is $$$\frac{20 x^{2}}{3} - \frac{20 x}{3} - \frac{370}{3} = 0$$$, so $$$a = \frac{20}{3}$$$, $$$b = - \frac{20}{3}$$$, $$$c = - \frac{370}{3}$$$.
Thus, $$$D = \left(- \frac{20}{3}\right)^{2} - \left(4\right)\cdot \left(\frac{20}{3}\right)\cdot \left(- \frac{370}{3}\right) = \frac{10000}{3}$$$.
Answer
The discriminant of $$$\frac{5 \left(2 x - 1\right)^{2}}{3} = 125$$$A is $$$\frac{10000}{3}\approx 3333.333333333333333$$$A.