For each equation, solve for x in terms of y. 2x² + 4xy - 3y² = 2

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$8x^2-72=0$

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) 4x² = -6x + 3

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) 3x² + 5x + 2 = 0

For each equation, (b) solve for y in terms of x. See Example 8.

$2x^2+4xy-3y^2=2$

For each equation, (b) solve for y in terms of x. See Example 8.

$4x^2-2xy+3y^2=2$

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.

$h=-16t^2+v_{0}t+s_0$, for t

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.

$r=r_0+\left(\frac{1}{2}\right)a{t}^2$, for t

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. $s=\left(\frac{1}{2}\right)g{t}^2$, for t