SOLUTION: 3X^2+2X-4=0

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Question 296809: 3X^2+2X-4=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2%2B2%2Ax-4=0 ( notice a=3, b=2, and c=-4)





x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29 Plug in a=3, b=2, and c=-4




x+=+%28-2+%2B-+sqrt%28+4-4%2A3%2A-4+%29%29%2F%282%2A3%29 Square 2 to get 4




x+=+%28-2+%2B-+sqrt%28+4%2B48+%29%29%2F%282%2A3%29 Multiply -4%2A-4%2A3 to get 48




x+=+%28-2+%2B-+sqrt%28+52+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%28-2+%2B+2%2Asqrt%2813%29%29%2F6 or x+=+%28-2+-+2%2Asqrt%2813%29%29%2F6



Now break up the fraction



x=-2%2F6%2B2%2Asqrt%2813%29%2F6 or x=-2%2F6-2%2Asqrt%2813%29%2F6



Simplify



x=-1%2F3%2Bsqrt%2813%29%2F3 or x=-1%2F3-sqrt%2813%29%2F3



So the solutions are:

x=-1%2F3%2Bsqrt%2813%29%2F3 or x=-1%2F3-sqrt%2813%29%2F3