If a,b,c $\in R$ , then roots of the quadratic equation
$x^{2} - 0.2 a x + a^{2} - b^{2} - c^{2} = 0$ are

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Solution

$x^{2} - 0.2 a x + a^{2} - b^{2} - c^{2} = 0$

$10 x^{2} - 2 a x + 10 a^{2} - 10 b^{2} - 10 c^{2} = 0$

We have a formula for solving quadratic equation $a x^{2} + b x + c = 0$ is

$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$x = \frac{- (- 2 a) \pm \sqrt{{(- 2 a)}^{2} - 4 \cdot 10 (10 a^{2} - 10 b^{2} - 10 c^{2})}}{2 \cdot 10}$

$x = \frac{a \pm \sqrt{100 b^{2} + 100 c^{2} - 99 a^{2}}}{10}$

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