Answer: x = 0.17 or x = -3.5
Step-by-step explanation:
The quadratic formula states [tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
We can then rearrange the equation given.
subtract 3[tex]x^{2}[/tex] from both sides to get -3[tex]x^{2}[/tex]+5x+8=0
From this you can see that our "a" term is -3[tex]x^{2}[/tex], our "b" term is 5x, and our "c" term is 8. (The "a" term always has the exponent in it, the "b" has just the variable and the coefficient, and the "c" is just a number)
We can then plug those numbers into our equation to get [tex]\frac{-(5x)±\sqrt{5^{2}-4(-3)(8) } }{2(-3)}[/tex]
[tex]5^{2}[/tex] = 25
4(-3)(8) = -96
Then simplify to get [tex]\frac{10±\sqrt{25-(-96) } }{-6}[/tex]
25 + 96 = 121
The square root of 121 is 11, so the new fraction becomes [tex]\frac{10±11}{-6}[/tex]
This can simplify to either [tex]\frac{-21}{6}[/tex], or -3.5 (this was using 10 + 11) or [tex]\frac{1}{6}[/tex] or 0.17 (using 10 - 11)
