Solve the given equation and find the value of $x$ -
$x^{2} + 2 a b = (2 a + b) x$

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Solution

Consider the following question.

$x^{2} + 2 a b = (2 a + b) x$

$Subtract (2 a + b) x from both sides$

$x^{2} + 2 a b - (2 a + b) x = (2 a + b) x - (2 a + b) x$

$x^{2} - (2 a + b) x + 2 a b = 0$

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

$x_{1, 2} = \frac{- (- 2 a - b) \pm \sqrt{{(- 2 a - b)}^{2} - 4 \cdot \times 1 \times 2 a b}}{2 \times 1}$

$x=2a, x=b$

Hence, this is the required answer.

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