Answer:
Yes I can. So I will.
Explanation:
Anytime you found yourself in doubt and danger about equations, you can use Geogebra Graph Calc - search for it -, and he will show you the graphic.
But, as I know that you are one the LAST HEROES IN EARTH, I pretty sure you don't want to just surrender yourself for a computer machine.
Let's calculate it:
4x² - 39x + 77
Bháskara Formula, you probably know her as Resolutive Formula, as she is known in my country, is:
![BF=\frac{-b \sqrt[]{b^2 - 4ac} }{2a}](https://img.qammunity.org/2021/formulas/mathematics/high-school/em0yrj52v50vq84hdv6xgau56u6xw76683.png)
there is also two signals + - betwen -b and the root.
She's one of the best ways to find roots for quadratic equations.
We will need to do that to find the interval required.
Also, remember that a generic quadratic equation can be describe as:
ax² + bx + c
So, knowing that in this equation
a = 4 / b = -39 / c = 77
We can proceed.
x' = - (-39) +
![\sqrt[]{(-39)^2 - 4.4.77}](https://img.qammunity.org/2021/formulas/mathematics/high-school/id5dclv0t27srfj035ix93902mvnm8izm3.png)
/ 2.4
x' = 39 + 17/ 8
x' = 7
x'' = 39 -17/8
x'' = 2,75
Now, you should know that when A > 0 the quadratic equation has her concavity facing down.
As we have the values of the roots, 7 and 2,75, we know that betwen them the equation has negative values.
That also means that all values higher than 7 and lower than 2,75 give to us a positive value.
Final answer:
x<2,75 and x>7
You will see in annex the graphic.