The Prince George's County Board of Education unanimously approved a $389 million budget last night for 1986-87, 11.5 percent above current spending, that would fully finance the county's magnet school plan for desegregation, hire 122 new teachers and reduce class size.

The budget does not earmark $615,000 for a high school for disruptive youths, marking the second time the board has rejected the facility proposed by Superintendent John A. Murphy. But the budget would finance programs designed to help students who have disciplinary and academic problems.

The budget includes $12.9 million to expand the program of magnet schools, which are designed to attract students by offering specialized instruction.

It calls for $2.5 million to create 122 new teaching positions to reduce average class size from 28 -- the highest in the state -- to 27.

The budget will be submitted to the County Council, which has until June 1 to act on it. It matches a proposal made this month by County Executive Parris Glendening.

Glendening, who had previously insisted on a ceiling of $380.7 million for county schools, announced Feb. 1 that he would make "internal adjustments" to the overall county budget to finance a school budget of $389 million. He did not specify what those adjustments would be.

The budget includes a $7.7 million "preliminary reserve," which a spokeswoman said would probably be used for teacher salary increases being negotiated.

Instead of funding a high school for disruptive students, the board approved $599,000 to expand Project Success, a remedial program designed to help ninth graders with disciplinary and academic problems. The program, started at Forestville, Potomac and Suitland high schools in September, would be expanded to include 10th graders at those schools and ninth graders at four unspecified high schools.

The board also allocated $100,000 to reinstitute supervised detention centers at three high schools yet to be determined. Those centers, used until recent years at junior high schools, give strict supervision to students identified as disruptive.

"There seemed to be significant community opposition to the alternative high school, particularly in the black community," said board Chairman Paul R. Shelby. "Although the superintendent tried to convince them that this was not a dumping ground for black students, that seemed to be the perception."

Board member Angelo Castelli, who had supported the proposed high school, said he went along with defeating it because "half of our [20] high schools will now have either in-house detention centers or Project Success. I'm thrilled with that."