Question 753459
Have you covered completing the square?
That's how I would do it.
{{{ 2x^2 + 4x - 7 = 0 }}}
Divide both sides by {{{ 2 }}}
{{{ x^2 + 2x - 7/2 = 0 }}}
Add {{{ 7/2 }}} to both sides
{{{ x^2 + 2x = 7/2 }}}
Take {{{ 1/2 }}} of the co-efficient of the
{{{ x }}} term, square it, then add it to 
both sides
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{{{ x^2 + 2x + ( 2/2 )^2 = 7/2 + ( 2/2 )^2 }}}
{{{ x^2 + 2x + 1 = 7/2 + 1 }}}
{{{ x^2 + 2x + 1 = 9/2 }}}
{{{ ( x + 1 )^2 = 9/2 }}}
Take the square root of both sides
{{{ x + 1 = 3 / sqrt(2) }}}
{{{ x = -1 + 3 / sqrt(2) }}}
and also
{{{ x + 1 = -3 / sqrt(2) }}}
{{{ x = -1 - 3 / sqrt(2) }}}
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These are the 2 answers. You can "clean them up"
by multiplying the 2nd term by {{{ sqrt(2) / sqrt(2) }}}
That will give you:
{{{ x = -1 + 3*sqrt(2) / 2 }}}
{{{ x = -1 - 3*sqrt(2) / 2 }}}
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Also, you can check both answers by plugging them
back into original equation. 
Hope this helps