Solve D/4=(-4k)^2+5*(4k^2-36)

$$\frac { D } { 4 } = ( - 4 k ) ^ { 2 } + 5 \times ( 4 k ^ { 2 } - 36 )$$

Solve for D

$$D=144\left(k^{2}-5\right)$$

Solution Steps

Multiply both sides of the equation by 4.

$$D=4\left(-4k\right)^{2}+20\left(4k^{2}-36\right)$$

Expand \left(-4k\right)^{2}.

$$D=4\left(-4\right)^{2}k^{2}+20\left(4k^{2}-36\right)$$

Calculate -4 to the power of 2 and get 16.

$$D=4\times 16k^{2}+20\left(4k^{2}-36\right)$$

Multiply 4 and 16 to get 64.

$$D=64k^{2}+20\left(4k^{2}-36\right)$$

Use the distributive property to multiply 20 by 4k^{2}-36.

$$D=64k^{2}+80k^{2}-720$$

Combine 64k^{2} and 80k^{2} to get 144k^{2}.

$$D=144k^{2}-720$$

Solve for k (complex solution)

$$k=-\frac{\sqrt{D+720}}{12}$$

$$k=\frac{\sqrt{D+720}}{12}$$

Solve for k

$$k=\frac{\sqrt{D+720}}{12}$$

$$k=-\frac{\sqrt{D+720}}{12}\text{, }D\geq -720$$