Question

5x^2=4x+7 quadratic equations by square method
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Answer 1

$\huge\underline{ \underline{ \bf{ \blue{ \: solution \: : = }}}} </p><p>$

by using quadratic formula,

$\bf {\boxed{\frac{ -b + - \sqrt{ {b }^{2} - 4ac} }{2a}}}$

⠀⠀⠀⟹⠀$x = \frac{ - ( - 4) + - \sqrt{ - 4 {}^{2} - 4 \times 5 \times ( - 7)} }{2 \times 5}$

⠀⠀⟹⠀⠀$x = \frac{ - 4 + - \sqrt{16 - 4 \times 5( - 7)} }{10}$

⠀⠀⠀⠀⟹⠀⠀$x = \frac{4 + - \sqrt{16 - 140} }{10}$

⠀⠀⠀⟹⠀⠀$x = \frac{4 + - \sqrt{156} }{10}$

⠀⠀⠀⠀⟹⠀⠀$x = \frac{4 + \times 2 \sqrt{39} }{10}$

⠀⠀⠀⠀⟹⠀⠀$x = \frac{2 \sqrt{39} + 4 }{10}$

⠀⠀⠀⟹⠀⠀${\bf{\boxed{\pink{x = \frac{ \sqrt{39} + 2}{ 5}}}}}$

⠀⠀⠀⠀⟹⠀$x = \frac{ - 4 - 2 \sqrt{39} }{10}$

⠀⠀⠀⠀⟹${\boxed{\pink{x = \frac{2 - \sqrt{39} }{5}}}}$

Answer 2

$completing \: square \: method.. \\ {5x}^{2} - 4x - 7 = 0 \\ divide \: with \: 5.. \\ { \frac{5x}{5} }^{2} - \frac{4x}{5} = \frac{7}{5} \\ add \: ({ \frac{2}{5} )}^{2} \: on \: both \: sides \\ {x}^{2} - \frac{4x}{5} + ({ \frac{2}{5} )}^{2} = \frac{7}{5} + ( { \frac{2}{5} )}^{2} \\( {x - \frac{2}{5} )}^{2} = \frac{7}{5} + \frac{4}{25} \\ x - \frac{2}{5} = \sqrt{ \frac{39}{25} } \\ x - \frac{2}{5} = \sqrt{ \frac{39}{5} } \\ x = \sqrt{39 \div 5 + \frac{2}{5} }$