Sure, let's solve the given quadratic equation step by step and find the values of [tex]\( x \)[/tex].
Given the equation:
[tex]\[
3x^2 - 7 = 140
\][/tex]
Step 1: Isolate the term with [tex]\( x^2 \)[/tex] by adding 7 to both sides of the equation.
[tex]\[
3x^2 - 7 + 7 = 140 + 7
\][/tex]
[tex]\[
3x^2 = 147
\][/tex]
Step 2: Solve for [tex]\( x^2 \)[/tex] by dividing both sides by 3.
[tex]\[
x^2 = \frac{147}{3}
\][/tex]
[tex]\[
x^2 = 49
\][/tex]
Step 3: Take the square root of both sides to solve for [tex]\( x \)[/tex].
[tex]\[
x = \pm \sqrt{49}
\][/tex]
[tex]\[
x = \pm 7
\][/tex]
So, the solutions are [tex]\( x = 7 \)[/tex] and [tex]\( x = -7 \)[/tex].
Thus, the answer is:
[tex]\[
\boxed{x=7,-7}
\][/tex]
