Solve -t^2+3/2t+1=y

$$- t ^ { 2 } + \frac { 3 } { 2 } t + 1 = y$$

Solve for y

$$y=-t^{2}+\frac{3t}{2}+1$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$y=-t^{2}+\frac{3}{2}t+1$$

Solve for t (complex solution)

$$t=\frac{-\sqrt{25-16y}+3}{4}$$

$$t=\frac{\sqrt{25-16y}+3}{4}$$

Solve for t

$$t=\frac{-\sqrt{25-16y}+3}{4}$$

$$t=\frac{\sqrt{25-16y}+3}{4}\text{, }y\leq \frac{25}{16}$$