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7x=2x²+1, solve the equation ​

User Swehren
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1 Answer

7 votes
7 votes

Answer:


x =(7+√(41))/(4),(7-√(41))/(4)

Explanation:

The given equation is ,


\longrightarrow 7x = 2x^2+1

We can rewrite it as ,


\longrightarrow 2x^2-7x + 1=0

On comparing with the standard form of quadratic equation
ax^2+bx + c , we have ;


  • a = 2

  • b = - 7

  • c = 1

On using the quadratic formula , we have;


\longrightarrow x = (-b \pm √(b^2-4ac))/(2a)\\


\longrightarrow x =(-(-7)\pm√((-7)^2-4(2)(1)))/(2(2)) \\


\longrightarrow x =(7\pm√(49-8))/(4)\\


\longrightarrow x =(7\pm√(41))/(4)

separate the solutions ,


\longrightarrow x =(7+√(41))/(4),(7-√(41))/(4)

And we are done !

User ENepper
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