Question 622805
<pre>
          x² = -3x + 1

Get 0 on the right:

 x² + 3x - 1 = 0 

Put a 1 coefficient for the x²

1x² + 3x - 1 = 0

Compare that to the general quadratic equation, which is

ax² + bx + c = 0

and you see that a=1, b=3, and c=-1

Substutute into this 

x = {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

x = {{{(-(3) +- sqrt( (3)^2-4*(1)*(-1) ))/(2*(1)) }}}

Simplify:

x = {{{(-3 +- sqrt(9+4 ))/2 }}}

x = {{{(-3 +- sqrt(13))/2 }}}

The ± symbol means that there are two answers, one using the +
and one using the - :

{{{(-3 + sqrt(13))/2 }}}, {{{(-3 - sqrt(13))/2 }}}

 

That's it.  Be sure to memorize 

ax² + bx + c = 0

and

x = {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

Edwin</pre>