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Discriminant of $$$10000000000 x^{2} = \frac{1}{100000000000} - x$$$
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Your Input
Find the discriminant of $$$10000000000 x^{2} = \frac{1}{100000000000} - x$$$.
Solution
Rewrite the equation: $$$10000000000 x^{2} = \frac{1}{100000000000} - x$$$ becomes $$$10000000000 x^{2} + x - \frac{1}{100000000000} = 0$$$.
The discriminant of the quadratic equation $$$a x^{2} + b x + c = 0$$$ is $$$D = b^{2} - 4 a c$$$.
Our equation is $$$10000000000 x^{2} + x - \frac{1}{100000000000} = 0$$$, so $$$a = 10000000000$$$, $$$b = 1$$$, $$$c = - \frac{1}{100000000000}$$$.
Thus, $$$D = 1^{2} - \left(4\right)\cdot \left(10000000000\right)\cdot \left(- \frac{1}{100000000000}\right) = \frac{7}{5}$$$.
Answer
The discriminant of $$$10000000000 x^{2} = \frac{1}{100000000000} - x$$$A is $$$\frac{7}{5} = 1.4$$$A.