SOLUTION: Please solve this equation with quadratic formula or other method (if possible) 〖-8y〗^2+2y+7=0 Workings very much appreciated, Sally

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Question 1021439: Please solve this equation with quadratic formula or other method (if possible)
〖-8y〗^2+2y+7=0
Workings very much appreciated,
Sally
Found 2 solutions by MathLover1, macston:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28-8y%29%5E2%2B2y%2B7=0
64y%5E2%2B2y%2B7=0

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A64%2A7%29%29%2F%282%2A64%29+
y+=+%28-2+%2B-+sqrt%28+4-1792%29%29%2F128+
y+=+%28-2+%2B-+sqrt%28+-1788%29%29%2F128+
y+=+%28-2+%2B-+2sqrt%28+447%29%2Ai%29%2F128+......simplify

y+=+%28-1+%2B-+sqrt%28+447%29%2Ai%29%2F64+
solutions:
y+=+%28-1+%2B+sqrt%28+447%29%2Ai%29%2F64+
or
y+=+%28-1+-+sqrt%28+447%29%2Ai%29%2F64+

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
-8y%5E2%2B2y%2B7=0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case -8y%5E2%2B2y%2B7+=+0) has the following solutons:

y%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=%282%29%5E2-4%2A-8%2A7=228.

Discriminant d=228 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+228+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%282%29%2Bsqrt%28+228+%29%29%2F2%5C-8+=+-0.818729304408844
y%5B2%5D+=+%28-%282%29-sqrt%28+228+%29%29%2F2%5C-8+=+1.06872930440884

Quadratic expression -8y%5E2%2B2y%2B7 can be factored:
-8y%5E2%2B2y%2B7+=+-8%28y--0.818729304408844%29%2A%28y-1.06872930440884%29
Again, the answer is: -0.818729304408844, 1.06872930440884. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B2%2Ax%2B7+%29