SOLUTION: I need to solve using quadratic formula 2x^2-3x=-6 the solution set is { } what I am coming up with is -(-3)+-sqrt57/4 but I am stuck after that any help would be appreciated

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Question 147088: I need to solve using quadratic formula 2x^2-3x=-6 the solution set is { }
what I am coming up with is
-(-3)+-sqrt57/4
but I am stuck after that
any help would be appreciated! Thank you
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need to solve using quadratic formula 2x^2-3x=-6 the solution set is { }
what I am coming up with is
-(-3)+-sqrt57/4
but I am stuck after that
------------------------------
2x^2-3x=-6
2x^2-3x+6 = 0
a = 2 ; b = -3 ; c = 6
---------
x = [3 +- sqrt(3 -4*2*6]/4
x = [3 +- sqrt(-45)]/4
x = [3 +- 3isqrt(5)]/4
x = (3/4)[1+isqrt(5)] or x = (3/4)[1 - isqrt(5)]
==========
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-3x=-6 Start with the given equation.


2x%5E2-3x%2B6=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-3, and c=6


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%282%29%286%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-3, and c=6


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%282%29%286%29+%29%29%2F%282%282%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%282%29%286%29+%29%29%2F%282%282%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-48+%29%29%2F%282%282%29%29 Multiply 4%282%29%286%29 to get 48


x+=+%283+%2B-+sqrt%28+-39+%29%29%2F%282%282%29%29 Subtract 48 from 9 to get -39


x+=+%283+%2B-+sqrt%28+-39+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%283+%2B-+i%2Asqrt%2839%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%283%2Bi%2Asqrt%2839%29%29%2F%284%29 or x+=+%283-i%2Asqrt%2839%29%29%2F%284%29 Break up the expression.


So our answers are x+=+%283%2Bi%2Asqrt%2839%29%29%2F%284%29 or x+=+%283-i%2Asqrt%2839%29%29%2F%284%29


which approximate to x=2.311%2Ai or x=-0.811%2Ai