Question

12 x raise to 2 - 15x + 3

Answer 1

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$

12x² - 15x + 3 = 0

$\LARGE\underline{\underline{\sf \red{S}\blue{o}\green{l}\orange{u}\pink{t}\purple{i}\orange{o}\red{n}:}}$

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$12 {x}^{2} - 15x + 3 = 0 \\ \\ 3 \times 4 {x }^{2} - 3 \times 5x + 3 = 0 \\ \\ multiply \: and \: divide \: by \: 3 \\ we \: get \\ \\ 3( \frac{3 \times 4 {x}^{2} }{3} - \frac{3 \times 5x}{3} + \frac{3}{3} ) = 0 \\ \\ 4 {x}^{2} - 5x + 1 = 0 \\ \\ 4 {x }^{2} - 4x - x + 1 = 0 \\ \\ 4x(x - 1) - 1(x - 1) = 0 \\ \\ (4x - 1)(x - 1) = 0 \\ \\ x = \frac{1}{4} \\ x \: = 1$

$\huge\underline\mathfrak\green{Hope\:it\:Helps\:You}$

Answer 2

$\huge\mathtt\purple{Solution}$

${12}^{2} - 15x + 3 \\ \\ here, using\: formula \:method \\ \\ \sf\implies\: a = 12 \\ \\ \sf\implies \: b = -15 \\ \\ \sf\implies \: c= 3 \\ \\ x = \frac{-b\sqrt{{b}^{2} - 4ac} } {2a} \\ \\ = \frac{-15 \sqrt{{(-15)}^{2} - 4 × 12 × 3} }{2 × 12} \\ \\ = \frac{-15 \sqrt {225 - 144}}{24} \\ \\ = \frac{-15\sqrt{81}}{24} \\ \\ = \frac{-15 +-9 } {24} \\ \\ taking + \\ \\ x = \frac{-15 + 9 }{24} \\ \\ x = \frac{-6}{24} \\ \\ x = \frac{-1}{4} \\ \\ taking - \\ \\ x = \frac{-15-9}{24} \\ \\ x = \frac{-24}{24} \\ \\ x = -1$

$\huge\boxed{x = \frac{-1}{4} , -1}$