Question

12x² + 7x = 10
Please solve using the quadratic formula.

Answer 1

12x² + 7x - 10 = 0

Quadratic Formula = D = b² - 4ac

= (7)² - 4(12)(-10)
= 49 + 480
= 529

Now 
 x = - b + √D   , x = -b - √D
          2a                   2a

x = -7 + 23      , x = -7 - 23
         24                     24

x = 16/24        , x = -30/24

x = 2/3            , x = -5/4

Answer 2

12x²+7x=10
or,12x²+7x-10
As the equation is of the form +,+,-,find mentally 2 numbers whose sum is +7 and product is 12*(-10)=-120.One number will be positive and the other negative such that +ve no. > -ve no. (As their sum is a postive number)Such numbers are +15 and -8.
Therefore,the equation can be written as:
12x²+15x-8x-10
factorizing the (1st and 2nd ) and (3rd and 4th) terms together,we get
3x(4x+5)-2(4x+5)
or,(3x-2)(4x+5)=0
Either 3x-2=0 or 4x+5=0
Either 3x=2 or 4x=-5
Either x=2/3 or x=-5/4
Ans:The 2 roots of the equation are: x=2/3 or -5/4.