Using the quadratic formula to solve 5x=6x^2-3, what are the values of x?
Accepted Solution
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Answer:Correct Choice: Second Option [tex]\displaystyle x=\frac{5\pm \sqrt{97}}{12}[/tex]Step-by-step explanation:Standard Form of Quadratic FunctionThe standard representation of a quadratic function is:[tex]f(x)=ax^2+bx+c[/tex]where a,b, and c are constants.Solving with the quadratic formula:[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]We have the following equation to solve:[tex]5x = 6x^2 -3[/tex]Rearranging all the terms to the left side:[tex]6x^2 -5x- 3=0[/tex]Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:[tex]\displaystyle x=\frac{-(-5)\pm \sqrt{(-5)^2-4(6)(-3)}}{2(6)}[/tex][tex]\displaystyle x=\frac{5\pm \sqrt{25+72}}{12}[/tex][tex]\boxed{\displaystyle x=\frac{5\pm \sqrt{97}}{12}}[/tex]Correct Choice: Second Option