Question 190085
10b^2-15b=8b-12   

Subtract the right-hand side of the equation from both sides:  

10b^2-15b-8b+12=0  

Now combine like terms:  

10b^2-23b+12=0 

Now it looks like we need the quadratic formula:  

-b/2a +-((b^2-4ac)^1/2)/2a, where a is the coeffient of the b^2 term,
b is the coefficient of the b term, and c is the coefficient of the
integer term.  So, a=10, b=-23, and c=12.  Plugging in the values gives us:  

b=23/20 +- (((-23)^2-(4)(10)(12))^1/2)/20.  We now have 
23/20 +-((529-480)^1/2)/20=23/20 +-((49)^1/2)/20=
23/20 +-7/20=30/20, 16/20=3/2, 4/5.  Check the answer by plugging in the
values:  10(3/2)^2-23(3/2)+12=0, 90/4-69/2+12=90/4-138/4=12=-48/4+48/4=0.
You can check the second result the same way.