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## Explanation

- Thrice the square of a natural number decreased by 4 times the number.

- Is equal to 50 more than the number.

The number can be figure out in this way.

Let suppose the number is y.

Thrice the square of “y” decreased by 4y

3y^{2 }– 4y

3y^{2 }– 4y is equal to 50 more than the number

3y^{2 }– 4y = y + 50 ________ (i)

Through equation (i) we can easily find out the value of y (y = 5).

## To Find

Number = ?

## Solution

Let suppose

Number = y

According to the given condition

3y^{2 }– 4y = y + 50

3y^{2 }– 4y – y – 50 = 0

3y^{2 }– 5y – 50 = 0

3y^{2 }– 15y + 10y – 50 = 0

3y(y – 5) + 10(y – 5) = 0

(3y + 10)(y – 5) = 0

3y + 10 = 0 & y – 5 = 0

y = -10/3 (not possible) & y = 5 (possible)

**Required Number = 5 answer**

## Conclusion

Thrice the square of a natural number decreased by 4 times, the number is equal to 50 more than the number. The number is 5.