Respuesta :
We have been given an equation [tex]x^{2\:}=\:9x\:+\:6[/tex]. We are asked to find the solution of our given equation.
We will use quadratic formula to solve our given problem.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
To apply quadratic formula, we need our equation in form [tex]ax^2+bc+c=0[/tex].
[tex]x^{2}-9x-6=9x-9x+6-6[/tex]
[tex]x^{2}-9x-6=0[/tex]
Now we can see that [tex]a=1,b=-9\text{ and }c=-6[/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]
[tex]x=\frac{9-\sqrt{105}}{2},\frac{9+\sqrt{105}}{2}[/tex]
Therefore, the solutions of our given equation are [tex]\frac{9-\sqrt{105}}{2},\frac{9+\sqrt{105}}{2}[/tex].
