# How do you Solve: 3x^2-2x=-5?

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to solve for : 3x^2 -2x = -5, this equation can be rewritten as

3x^2 -2x+5 = 0

it is a quadratic equation in x

for ax^2+bx+c = 0 , we have x= (-b +- `sqrt(b^2-4ac)` )/2a

compare the given equation with the standard form we get

a= 3 ,b =-2 and c= 5, plug in a,b,c to get x

x = ( -(-2) +- `sqrt((-2)^2 - 4.3.5)` ) / 2.3

= (4 +- `sqrt(4- 60)` ) / 6

= (4 +- `sqrt(-56)` ) / 6 =( 4 +- `sqrt(-1 * 4* 14)` )/6

= (4 +- 2i`sqrt(14)` )/6, (as sqrt(-1) = i) = (2 +- i`sqrt(14)` ) / 3

thus x = ( 2+i`sqrt(14)` )/3 or (2- i`sqrt(14)` ) /3

I think -b = -(-2) = 2

so the answer should be ( 1+i )/3 or (1- i ) /3