## anonymous one year ago Solve the Quadratic: 3x^2+10x-8=0

1. SolomonZelman

$$\large\color{black}{ {\rm Discriminant}=\sqrt{b^2-4(a)(c)} \\[1.2em]=\sqrt{10^2-4(3)(-8)}=\sqrt{100-(-96)} =\sqrt{196}=14}$$

2. anonymous

Dont you have to divide it by 2a?

3. SolomonZelman

You can either solve your equation using the *quadratic formula* (I have calculated the discriminant for you) OR, you can factor, because the discriminant is an integer and thus your quadratic can be factored.

4. anonymous

I tried factoring but I got confused

5. SolomonZelman

*QUADRATIC FORMULA* $$\normalsize\color{ slate }{\Huge{\bbox[5pt, lightcyan ,border:2px solid black ]{ \LARGE{x=~} \huge{ \frac{-\color{magenta}{b} \pm\sqrt{ \color{magenta}{b} ^2-4 \color{blue}{a} \color{red}{c}}}{2 \color{blue}{a}} }~ }}}$$ when the equation is $$\LARGE\color{black}{ \color{blue}{a} x^2+ \color{magenta}{b}x+ \color{red}{c}=0 }$$

6. anonymous

Could you help me with factoring?

7. SolomonZelman

you already know that: $$\large \displaystyle x=\frac{-\color{magenta}{10} \pm14}{2 \color{blue}{(3)}}$$

8. SolomonZelman

14 is the value of that entire root, which I calculated in the beginning, and you know that in your case, *a=3* and *b=10*

9. anonymous

so is there two answers?Because +- 14

10. SolomonZelman

yes, and they are simplifiable.

11. SolomonZelman

you can do the rest....

12. anonymous

2/3 and -4?

13. SolomonZelman

yes, right

14. anonymous

thanks