Solve 4a^2-12*7a<0

$$4 a ^ { 2 } - 12 \times 7 a < 0$$

Solve for a

$$a\in \left(0,21\right)$$

Solution Steps

Multiply 12 and 7 to get 84.

$$4a^{2}-84a<0$$

Factor out a.

$$4a\left(a-21\right)<0$$

For the product to be negative, a and a-21 have to be of the opposite signs. Consider the case when a is positive and a-21 is negative.

$$a>0 a-21<0$$

The solution satisfying both inequalities is a\in \left(0,21\right).

$$a\in \left(0,21\right)$$

Consider the case when a-21 is positive and a is negative.

$$a-21>0 a<0$$

This is false for any a.

$$a\in \emptyset$$

The final solution is the union of the obtained solutions.

$$a\in \left(0,21\right)$$