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use the quadratic formula to solve 3v^2+4v-1=0

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To solve by quadratic formula you must first make sure all the terms are on one side of the equation and it is set equal to zero. Also make sure the terms are arranged from highest power to lowest.
 
The coefficient (number) in front of the first term is a
The coefficient (number) in front of the second term is b
The coefficient (number) in front of the third term is c
 
For this problem  3V2 +4V -1 =0     a= 3      b= 4  and c= -1
                                                          __________
Use the formula    -b  +/- √ b2 - 4ac
                                   2a
                                   ____________
This gives you  -4  +/- √(4)2 - 4(3)(-1)
                                  2(3)
                                   _________                                  _______
                      -4  +/- √ 16 - (-12)           ⇒        -4  +/- √ 16 +12            
                                   6                                             6
                                    
                                    ___
                       -4  +/- √ 28        ( 28 can be factored into 4 times 7 and 4 is a perfect square that comes
                              6                    out to the front of the radican as a 2)
                                      __
                       -4  +/- 2√ 7
                              6
                                     ___                                 ____
                     -4  +/-  2√ 7             ⇒     -2   +/-  √   7
                      6           6                         3              3