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Find the value of x satisfying/ : $ 5(2x^2 − 7) − 2(5x^2 + 8x − 2) = 12 $

Find the value of x satisfying / x का वह मान ज्ञात कीजिए जो निम्नलिखित समीकरण को संतुष्ट करता है। :
$ 5(2x^2 − 7) − 2(5x^2 + 8x − 2) = 12 $

$-\frac{43}{16}$ $-\frac{39}{16}$ $-\frac{53}{16}$ $-\frac{49}{16}$

Detailed Solution & Logic

Correct Answer:

$-\frac{43}{16}$

Given equation: $5(2x^2 − 7) − 2(5x^2 + 8x − 2) = 12$

Expand:
$5(2x^2 − 7) = 10x^2 − 35$
$2(5x^2 + 8x − 2) = 10x^2 + 16x − 4$

Substitute:
$10x^2 − 35 − (10x^2 + 16x − 4) = 12$

Simplify:
$10x^2 − 35 − 10x^2 − 16x + 4 = 12$
$-16x − 31 = 12$

$-16x = 43$
$x = -\frac{43}{16}$

$-\frac{43}{16}$

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