Question 1207404
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<pre>

The short answer to your question is "Yes".



But there is another way, much more attractive.


Multiply all the terms of your equation by 4.


You will get then other, EQUIVALENT quadratic equation

    3x^2 - x - 2 = 0.


Apply now the quadratic formula, which you know

    {{{x[1,2]}}} = {{{(1 +- sqrt((-1)^2 - 4*3*(-2)))/(2*3)}}} = {{{(1 +- sqrt(25))/6}}}.


Thus  {{{x[1]}}} = {{{(1 + sqrt(25))/6}}} = {{{(1 + 5)/6}}} = 1

and   {{{x[2]}}} = {{{(1 - sqrt(25))/6}}} = {{{(1 - 5)/6}}} = {{{-4/6}}} = {{{-2/3}}}.


So, the solutions are the numbers  1  and   {{{-2/3}}}.
</pre>

Solved.


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On solving quadratic equations using the quadratic formula, &nbsp;see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

in this site.