Solve f-3/6-2t^4-5=5

$$\frac { f - 3 } { 6 - 2 t ^ { 4 } - 5 } = 5$$

Solve for f

$$f=8-10t^{4}$$

$$t\neq -\frac{2^{\frac{3}{4}}}{2}\text{ and }|t|\neq \frac{2^{\frac{3}{4}}}{2}$$

Solution Steps

Multiply both sides of the equation by -2t^{4}+1.

$$f-3=5\left(-2t^{4}+1\right)$$

Use the distributive property to multiply 5 by -2t^{4}+1.

$$f-3=-10t^{4}+5$$

Add 3 to both sides.

$$f=-10t^{4}+5+3$$

Add 5 and 3 to get 8.

$$f=-10t^{4}+8$$

Solve for t

$$t=\frac{10^{\frac{3}{4}}\sqrt[4]{8-f}}{10}$$

$$t=-\frac{10^{\frac{3}{4}}\sqrt[4]{8-f}}{10}\text{, }f\neq 3\text{ and }f\leq 8$$