Solve Delta=left(-12pright)^2-4.9p^2-4

$$\Delta = { \left(-12p \right) }^{ 2 } -4.9 { p }^{ 2 } -4$$

Solve for Δ

$$\Delta =\frac{1391p^{2}}{10}-4$$

Solution Steps

Expand \left(-12p\right)^{2}.

$$\Delta =\left(-12\right)^{2}p^{2}-4.9p^{2}-4$$

Calculate -12 to the power of 2 and get 144.

$$\Delta =144p^{2}-4.9p^{2}-4$$

Combine 144p^{2} and -4.9p^{2} to get 139.1p^{2}.

$$\Delta =139.1p^{2}-4$$

Solve for p

$$p=\frac{\sqrt{\frac{40\Delta +160}{1391}}}{2}$$

$$p=-\frac{\sqrt{\frac{40\Delta +160}{1391}}}{2}\text{, }\Delta \geq -4$$