Hello, Chief343!

Designate an variable for an unknown quantity.

Then

*try* to tranlate the English into an equation.

1) Twice the square of a number minus 3 is 47. \(\displaystyle \;\) Find the number.

Let \(\displaystyle x\) = the number.

\(\displaystyle \;\;\underbrace{Twice}\;\underbrace{the\;square\;of\;a\;number}\;\underbrace{minus}\;3\;\underbrace{is}\;47.\)

. . . . \(\displaystyle 2\)

. . . . . . \(\displaystyle \times\)

. . . . . . \(\displaystyle x^2\)

. . . . . . . . . . . . . \(\displaystyle \,-\;\;\;3\;=\;47\)

And there is our equation! \(\displaystyle \;2x^2\,-\,3\;=\;47\)

I assume you can finish it now . . .

2) The product of 2 consecutive even positive integers is 120. \(\displaystyle \;\) Find the integers.

Consecutive even integers "go up by twos" (so do odd integers).

Let \(\displaystyle x\) = first even integer.

Then \(\displaystyle x\,+\,2\) = next even integer.

\(\displaystyle \;\;\underbrace{The\;product\;of\;two\;c.e.p.\;integers}\;\underbrace{is}\;120\)

. . . . . . . . . . . . . . . \(\displaystyle x(x\,+\,2)\)

. . . . . . . . . . . . . . \(\displaystyle =\;120\)

And we have our equation: \(\displaystyle \;x(x\,+\,2)\;=\;120\)

\(\displaystyle \;\;\)

*Go for it!*