Question

Solve for x: 3x to the second power+ 7x=2

Answer 1

\(\sf 3x \color{red}{^2}+7x=2 \Rightarrow 3x^2+7x-2=0\)

Answer 2

dont know where to go from there

Answer 3

You need to use this thing called discriminant and equation it is used in
http://en.wikipedia.org/wiki/Discriminant

Answer 4

for discriminant in school we used letter d, so i will use it there also
you have this equation 3x^2 +7x - 2 = 0 , but to determine letters in later used formulass you must first know this example: ax^2 +bx +c = 0 , from wich you get that your's a is equal 3, b is equal 7 and c is equal -2, now determinant
d = b^2 -4ac
there is also a quick way to tell how many variants of x you will have y finding value of determinant
d >0 means you have 2 variants
d = 0 means you have one
d< 0 means equation can not be solved or is somewhat wicked

Answer 5

as for when you have found value of determinant (given your discriminant value is more then zero), you now can use these formulas:
x1 = (-b + squareroot(d) )/2a and x2 = (-b - squareroot(d) )/2a

second case - so, if discriminant is value 0, then you square root zero, meaning x1=x2

last case - since you can't "pull" square root from negative number, then x cannot be found