Answer:
[tex]x=\frac{9\pm \sqrt{105}}{2}[/tex]
Step-by-step explanation:
We have been given a quadratic equation [tex]x^2=9x+6[/tex]. We are asked to find the solutions of our given equation.
First of all, we will gather all terms on one side of equation as:
[tex]x^2-9x-6=9x-9x+6-6[/tex]
[tex]x^2-9x-6=0[/tex]
Now, we will use quadratic formula to solve for x as:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-9)\pm \sqrt{(-9)^2-4(1)(-6)}}{2(1)}[/tex]
[tex]x=\frac{9\pm \sqrt{81+24}}{2}[/tex]
[tex]x=\frac{9\pm \sqrt{105}}{2}[/tex]
Therefore, the solutions of our given equation are [tex]x=\frac{9\pm \sqrt{105}}{2}[/tex].
