Solve z^2+3t/2=t+7/4

$$\frac { z ^ { 2 } + 3 t } { 2 } = \frac { t + 7 } { 4 }$$

Solve for t

$$t=\frac{7-2z^{2}}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(z^{2}+3t\right)=t+7$$

Use the distributive property to multiply 2 by z^{2}+3t.

$$2z^{2}+6t=t+7$$

Subtract t from both sides.

$$2z^{2}+6t-t=7$$

Combine 6t and -t to get 5t.

$$2z^{2}+5t=7$$

Subtract 2z^{2} from both sides.

$$5t=7-2z^{2}$$

Divide both sides by 5.

$$\frac{5t}{5}=\frac{7-2z^{2}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$t=\frac{7-2z^{2}}{5}$$

Solve for z (complex solution)

$$z=-\frac{\sqrt{14-10t}}{2}$$

$$z=\frac{\sqrt{14-10t}}{2}$$

Solve for z

$$z=\frac{\sqrt{14-10t}}{2}$$

$$z=-\frac{\sqrt{14-10t}}{2}\text{, }t\leq \frac{7}{5}$$