Answer:
Correct Choice: Second Option
[tex]\displaystyle x=\frac{5\pm \sqrt{97}}{12}[/tex]
Step-by-step explanation:
Standard Form of Quadratic Function
The 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
