SOLUTION: 2x^2=3x+3

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Question 147128: 2x^2=3x+3
Found 2 solutions by nabla, jim_thompson5910:
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2=3x+3
2x^2-3x-3=0
Apply quadratic formula.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-3=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+33+%29%29%2F2%5C2+=+2.18614066163451
x%5B2%5D+=+%28-%28-3%29-sqrt%28+33+%29%29%2F2%5C2+=+-0.686140661634507

Quadratic expression 2x%5E2%2B-3x%2B-3 can be factored:
2x%5E2%2B-3x%2B-3+=+2%28x-2.18614066163451%29%2A%28x--0.686140661634507%29
Again, the answer is: 2.18614066163451, -0.686140661634507. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-3+%29

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

2x%5E2=3x%2B3 Start with the given equation.


2x%5E2-3x-3=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=-3


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%28-3%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-3, and c=-3


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


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


x+=+%283+%2B-+sqrt%28+9--24+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-3%29 to get -24


x+=+%283+%2B-+sqrt%28+9%2B24+%29%29%2F%282%282%29%29 Rewrite sqrt%289--24%29 as sqrt%289%2B24%29


x+=+%283+%2B-+sqrt%28+33+%29%29%2F%282%282%29%29 Add 9 to 24 to get 33


x+=+%283+%2B-+sqrt%28+33+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%283%2Bsqrt%2833%29%29%2F%284%29 or x+=+%283-sqrt%2833%29%29%2F%284%29 Break up the expression.


So our answers are x+=+%283%2Bsqrt%2833%29%29%2F%284%29 or x+=+%283-sqrt%2833%29%29%2F%284%29


which approximate to x=2.186 or x=-0.686