using the quadratic formula to solve 5x = 6x² - 3, what are the values of x?\n$\frac{5pm3sqrt{11}}{12}$\n$\fr…

using the quadratic formula to solve 5x = 6x² - 3, what are the values of x?\n$\frac{5pm3sqrt{11}}{12}$\n$\frac{5pmsqrt{97}}{12}$\n$\frac{5pmsqrt{47}}{12}$\n$\frac{-5pmsqrt{97}}{12}$

using the quadratic formula to solve 5x = 6x² - 3, what are the values of x?\n$\frac{5pm3sqrt{11}}{12}$\n$\frac{5pmsqrt{97}}{12}$\n$\frac{5pmsqrt{47}}{12}$\n$\frac{-5pmsqrt{97}}{12}$

Answer

Explanation:

Step1: Rearrange to standard form

First, rewrite the equation $5x = 6x^{2}-3$ as $6x^{2}-5x - 3=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 6$, $b=-5$, $c=-3$.

Step2: Recall quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Calculate discriminant

Calculate $b^{2}-4ac=(-5)^{2}-4\times6\times(-3)=25 + 72=97$.

Step4: Substitute values

Substitute $a = 6$, $b=-5$, and $b^{2}-4ac = 97$ into the quadratic formula: $x=\frac{-(-5)\pm\sqrt{97}}{2\times6}=\frac{5\pm\sqrt{97}}{12}$.

Answer:

$\frac{5\pm\sqrt{97}}{12}$