Respuesta :
Answer:
[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex]
Step-by-step explanation:
First step is to arrange so it is in the form [tex]ax^2+bx+c=0[/tex].
We have [tex]5x=6x^2-3[/tex].
Add we really need to do is subtract 5x on both sides:
[tex]0=6x^2-5x-3[/tex].
Now let's compare [tex]6x^2-5x-3[/tex] to [tex]ax^2+bx+c[/tex].
We have [tex]a=6,b=-5,c=-3[/tex].
The quadratic formula is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
I like to break this into parts:
Part 1: Find [tex]-b[/tex].
Part 2: Find [tex]b^2-4ac[/tex].
Part 3: Find [tex]2a[/tex].
Answering the parts:
Part 1: [tex]-b=5[/tex] since [tex]b=-5[/tex].
Part 2: [tex]b^2-4ac=(-5)^2-4(6)(-3)=25-24(-3)=25+72=97[/tex].
Part 3: [tex]2a=2(6)=12[/tex].
Now our formula in terms of my parts looks like this:
[tex]x=\frac{\text{Part 1} \pm \sqrt{Part 2}}{Part 3}[/tex]
Our formula with my parts evaluated looks like this:
[tex]x=\frac{5 \pm \sqrt{97}}{12}[/tex].
