2x^2+4x-7=0

2x^2 + 4x - 7 = 0

Add 7 to both sides

2x^2 + 4x  =   7       divide through by 2

x^2 + 2x  = 7/2 

Take (1/2) of the coefficient on x  = (1/2)(2)  = 1

Square this  = 1   and add it to both sides

x^2 + 2x + 1  =  7/2 + 1        factor the left and simpify the right

(x + 1)^2  =   9/2                  take both roots

x + 1  =   ±√ [9/2]

x + 1  = ±3 /√2        rationalize the denominator on the righr

x + 1  =  ±3√2  / 2      subtract 1 from both sides

x =  ±3√2  / 2  -  1

x = ±3√2  / 2  - 2/2

x = [ -2  ± 3√2 ]   / 2

- Aiyan