Answer:

m1= -17/2, m2= 3/2 or m1= -8.5, m2= 1.5

Step-by-step explanation:

m2+ 7m- 51/4=0

Multiply both sides of equation by 4

4m2+ 28m- 51= 0

write 28m as a difference

4m2= 34m-6m-51=0

factor out 2m from the expression

2m x (2m+17)-6m-51=0

factor out -3 from the expression

2m x (2m+ 17)-3(2m+ 17)=0

factor out 2m+17 from the expression

(2m+17) x(2m-3)=0

when the product of factors equals 0, at least one factor is 0

2m+17=0  

2m-3=0

solve the equation for m

m= -17/2

2m-3=0

solve the equation for m

m= -17/2

m= 3/2

the equation has 2 solutions

m1= -17/2, m2= 3/2

alternative form:

m1= -8.5, m2= 1.5