Question 196128
2x^2=5x+7 First, we need to put this quadratic equation in standard form:
subtract 5x+7 from both sides:  2x^2-5x-7=0.  We use the quadratic equation because it cannot be easily factored.  The quadratic equation is x=
-b/2a+-((b^2-4ac)^1/2/2a), where a is the coefficient of the x^2 term, b is the
coefficient of the x term, and c is the integral term.  We have a=2, b=-5, and c=-7.  Plugging in the values, x=5/2*2+-(25-4*2*-7)^1/2/2*2=5/4+-(25+56)^1/2/4,
x=(5+(81)^1/2)/4=14/4=7/2, x=(5-(81)^1/2)/4=-4/4=-1.  Let's plug in x=-1 to see if we have it correct:  2(-1)^2-5(-1)-7=2+5-7=0, it is correct, x=-1 is a root.  
You can plug in x=7/2 to see if it is a root.