Question 1165410
<pre>
To start, I assume you meant that 'y' to be 'x': {{{ 4.6x^2 + 3.5x - 1.75 = 0 }}}

Multiply by 100:
{{{ 460x^2 + 350x - 175 = 0}}}

Reduce (divide by 5):
{{{ 92x^2 + 70x - 35 = 0 }}}

Divide by 92:
{{{  x^2 + (70/92)x - (35/92) = 0 }}}
{{{ x^2 + (70/92)x = 35/92 }}}

Add {{{ ((1/2)(70/92))^2 }}} to both sides:
{{{ x^2 + (70/92)x + (35/92)^2 = (35/92) + (35/92)^2 }}}

{{{ (x+(35/92))^2 =   (35/92) + (35/92)^2 }}}

Take the square root of both sides, this introduces +/- on RHS:
{{{  x+(35/92) }}} = +/- {{{sqrt((35/92)+(35/92)^2) }}} 
{{{  x }}} =  - {{{35/92}}} +/- {{{sqrt((35/92)+(35/92)^2) }}} 

This evaluates to the solutions:
   x = 0.34425
   x = -1.10512