Question

solve the quadratic equation 3x2=2x+8 using formula method​

Answer 1

Step-by-step explanation:

3×2=2x+8

6=2x+8

-2x=8-6 ans:-1

-2x=2

X=2/-2

X= -1

Answer 2

$\sf{\underline{\boxed{\green{\large{\bold{ Question}}}}}}$

• solve the equation using formulae $\sf 3x^2 = 2x + 8$

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$\sf{\underline{\boxed{\green{\large{\bold{ Solution}}}}}}$

$\sf\implies 3x^2 = 2x + 8$

$\sf\implies 3x^2 - 2x - 8= 0$

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• compare the eq with $\sf{\underline{\bold{ax^2 + bx + c = 0 }}}$

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☯ a = 3

☯ b = -2

☯ c = -8

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now :-

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{x = \dfrac{ - b \pm \sqrt D }{2a }}}}}}}$

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{ D = b^2 - 4ac }}}}}}$

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• finding value of D.

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$\sf\implies D = b^2 - 4ac$

$\sf\implies D = (-2)^2 - 4 \times 3 \times -8$

$\sf\implies D = 4 + 96$

$\sf\implies D = 100$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = 100}}}}}}$

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• putting values in the eq.

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$\sf\implies x = \dfrac{ -b \pm\sqrt D }{2a}$

$\sf\implies x = \dfrac{ -( -2) \pm\sqrt {100} }{2\times 3 }$

$\sf\implies x = \dfrac{ 2\pm 10 }{6}$

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✒$\sf x = \dfrac{ 2 + 10 }{ 6 }$

$\implies x = \dfrac {12}{6}$

$\implies x = 2$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = 2 }}}}}}$

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✒$\sf x = \dfrac{ 2 - 10 }{ 6 }$

$\implies x = \dfrac {-8}{6}$

$\implies x = \dfrac{-4}{3}$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = \dfrac{-4}{3} }}}}}}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = 2 \: or \:\dfrac{-4}{3} }}}}}}$