Hello friends! Welcome to math and science channel.
We solve an exercise on quadratic equations
using the quadratic formula.
This time, we will solve this equation by
noting that the coefficient of the quadratic term is different from 1. This coefficient is 3.
Furthermore, the coefficients of this equation, 3, 6 y 180
have a common factor that can be extracted, this is done by dividing the equation by this common factor.
If you notice it, the common factor is 3.
We must identify "a" is 3, "b" is 6 and "c" is -180.  That is, we divide equation by 3.
we get the following
3x squared, divided by 3, is x squared. 
6x divided by 3 is 2x. 
-180 divided by 3, is -60.
0 divided by 3, is 0.
In this equation, We apply the quadratic formula. We have obtained new coefficients. 
b is +2.
c is -60.
a is 1.
You wonder if I can apply the quadratic formula with coefficients 3, 6 and -180.
The answer is yes. This is right.
But we must observe, that the new coefficients are lower than those shown above.
This gives us the advantage to apply the  quadratic formula.
Numerical calculation is easier now.
We write the quadratic formula.
We must begin the replacement of the new coefficients into the quadratic formula.
-b is -2 
Plus, minus, square root of 2 squared minus 4 multiplied by 1 and -60
All divided by 2 multiplied by 1.
The square root of 244 is not an integer. That is, it is not a perfect square number. Therefore, we decompose 244, into prime factors.
First, half of 244, is 122.
Then half of 122, is 61.
61 is a prime number.
Then we can express 244 as the product of
4 and 61.
We extract the square root of 4, is 2.
61 is maintained within the radical because...
it is not a perfect square number.
We extract a common factor in the numerator, 2.
Delete this common factor with the number 2 in the denominator.
The first root 
is 1 + the square root of 61.
The second root is: -1 - the square root of
61.
In other videos on this channel, we calculate the square root of a perfect square number, but in this video, this changed.
Subscribers asked me to prepare a video, where to find the square root of a number that is not a perfect square.
Well, I hope you enjoyed this video. 
If so, then do not forget to click the button "I like".
Or you can share it with your friends.
If you want more videos like other mathematical topics, subscribe to this channel
you will see new videos weekly.
These videos are designed to help in the study of mathematics.
And later, also in physics or chemistry.
Thank you for your attention.
