Solve Delta=(lambda-4)^2-4*2*(-lambda)

$$\Delta = ( \lambda - 4 ) ^ { 2 } - 4 \cdot 2 \cdot ( - \lambda )$$

Solve for Δ

$$\Delta =\lambda ^{2}+16$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\lambda -4\right)^{2}.

$$\Delta =\lambda ^{2}-8\lambda +16-4\times 2\left(-\lambda \right)$$

Multiply 4 and 2 to get 8.

$$\Delta =\lambda ^{2}-8\lambda +16-8\left(-\lambda \right)$$

Multiply -1 and 8 to get -8.

$$\Delta =\lambda ^{2}-8\lambda +16-8\left(-1\right)\lambda$$

Multiply -8 and -1 to get 8.

$$\Delta =\lambda ^{2}-8\lambda +16+8\lambda$$

Combine -8\lambda and 8\lambda to get 0.

$$\Delta =\lambda ^{2}+16$$

Solve for λ (complex solution)

$$\lambda =-\sqrt{\Delta -16}$$

$$\lambda =\sqrt{\Delta -16}$$

Solve for λ

$$\lambda =\sqrt{\Delta -16}$$

$$\lambda =-\sqrt{\Delta -16}\text{, }\Delta \geq 16$$