Solve x/1=-t^2+3t+4/5-t

$$\frac { x } { 1 } = \frac { - t ^ { 2 } + 3 t + 4 } { 5 - t }$$

Solve for x

$$x=-\frac{\left(t-4\right)\left(t+1\right)}{5-t}$$

$$t\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -t+5.

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

The equation is in standard form.

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

Divide both sides by 5-t.

$$\frac{\left(5-t\right)x}{5-t}=-\frac{\left(t-4\right)\left(t+1\right)}{5-t}$$

Dividing by 5-t undoes the multiplication by 5-t.

$$x=-\frac{\left(t-4\right)\left(t+1\right)}{5-t}$$

Solve for t (complex solution)

$$t=\frac{\sqrt{x^{2}-14x+25}+x+3}{2}$$

$$t=\frac{-\sqrt{x^{2}-14x+25}+x+3}{2}$$

Solve for t

$$t=\frac{\sqrt{x^{2}-14x+25}+x+3}{2}$$

$$t=\frac{-\sqrt{x^{2}-14x+25}+x+3}{2}\text{, }x\geq 2\sqrt{6}+7\text{ or }x\leq 7-2\sqrt{6}$$