SOLUTION: How do you solve 3x=-x^2+8

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Question 485589: How do you solve 3x=-x^2+8
Found 2 solutions by jorel1380, deborabr:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
3x=-x^2+8
x2+3x-8=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-8+=+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=%283%29%5E2-4%2A1%2A-8=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+41+%29%29%2F2%5C1+=+1.70156211871642
x%5B2%5D+=+%28-%283%29-sqrt%28+41+%29%29%2F2%5C1+=+-4.70156211871642

Quadratic expression 1x%5E2%2B3x%2B-8 can be factored:
1x%5E2%2B3x%2B-8+=+1%28x-1.70156211871642%29%2A%28x--4.70156211871642%29
Again, the answer is: 1.70156211871642, -4.70156211871642. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-8+%29
..

Answer by deborabr(181) About Me  (Show Source):
You can put this solution on YOUR website!
3x=-x^2+8
this is an equation of the second degree
we pass the members of the right to the left changing the signals positive to negative and vice versa.Now we equate to zero.
x^2+3x-8=0
where representing:
1=a --> is the value or number that folows X^2 and when it's 1 doesn't need show
3=b --> is the value or number that folows x
-8=c --> is the value or number single, but don't forget the signal
Now we use the formula: delta =(b)^2-4*a*c
substituting
delta=(3)^2-4(1)(-8)
delta=(3*3)-4(-8)--> ps:-4(-8), - with - equal +
delta=9+32
delta=41
Use the second formula: x=-(b)/2(a)+/-root delta/2(a)
Applying it:
x=-3/2+/-root 41/2
answers:
1°x=-3/2+root 41/2
2°x=-3/2-root 41/2